SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1369-1380, June 2024. Abstract. We estimate the likely values of the chromatic and independence numbers of the random [math]-uniform [math]-regular hypergraph on [math] vertices for fixed [math], large fixed [math], and [math].
{"title":"On the Chromatic Number of Random Regular Hypergraphs","authors":"Patrick Bennett, Alan Frieze","doi":"10.1137/22m1544476","DOIUrl":"https://doi.org/10.1137/22m1544476","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1369-1380, June 2024. <br/>Abstract. We estimate the likely values of the chromatic and independence numbers of the random [math]-uniform [math]-regular hypergraph on [math] vertices for fixed [math], large fixed [math], and [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1351-1368, June 2024. Abstract. Many important problems in extremal combinatorics can be stated as certifying polynomial inequalities in graph homomorphism numbers, and in particular, many ask to certify pure binomial inequalities. For a fixed collection of graphs [math], the tropicalization of the graph profile of [math] essentially records all valid pure binomial inequalities involving graph homomorphism numbers for graphs in [math]. Building upon ideas and techniques described by Blekherman and Raymond in 2022, we compute the tropicalization of the graph profile for the graph containing a single vertex as well as stars where one edge is subdivided. This allows pure binomial inequalities in homomorphism numbers (or densities) for these graphs to be verified through an explicit linear program where the number of variables is equal to the number of edges in the biggest graph involved.
{"title":"Tropicalizing the Graph Profile of Some Almost-Stars","authors":"Maria Dascălu, Annie Raymond","doi":"10.1137/23m1594947","DOIUrl":"https://doi.org/10.1137/23m1594947","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1351-1368, June 2024. <br/> Abstract. Many important problems in extremal combinatorics can be stated as certifying polynomial inequalities in graph homomorphism numbers, and in particular, many ask to certify pure binomial inequalities. For a fixed collection of graphs [math], the tropicalization of the graph profile of [math] essentially records all valid pure binomial inequalities involving graph homomorphism numbers for graphs in [math]. Building upon ideas and techniques described by Blekherman and Raymond in 2022, we compute the tropicalization of the graph profile for the graph containing a single vertex as well as stars where one edge is subdivided. This allows pure binomial inequalities in homomorphism numbers (or densities) for these graphs to be verified through an explicit linear program where the number of variables is equal to the number of edges in the biggest graph involved.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Laurent Bulteau, Konrad K. Dabrowski, Noleen Köhler, Sebastian Ordyniak, Daniël Paulusma
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1315-1350, June 2024. Abstract. A homomorphism [math] from a guest graph [math] to a host graph [math] is locally bijective, injective, or surjective if for every [math], the restriction of [math] to the neighbourhood of [math] is bijective, injective, or surjective, respectively. We prove a number of new FPT (fixed-parameter tractable), W[1]-hard, and paraNP-complete results for the corresponding decision problems LBHom, LIHom, and LSHom by considering a hierarchy of parameters of the guest graph [math]. In this way we strengthen several existing results. For our FPT results, we develop a new algorithmic framework that involves a general ILP (integer linear program) model. We also use our framework to prove FPT results for the Role Assignment problem, which originates from social network theory and is closely related to locally surjective homomorphisms.
{"title":"An Algorithmic Framework for Locally Constrained Homomorphisms","authors":"Laurent Bulteau, Konrad K. Dabrowski, Noleen Köhler, Sebastian Ordyniak, Daniël Paulusma","doi":"10.1137/22m1513290","DOIUrl":"https://doi.org/10.1137/22m1513290","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1315-1350, June 2024. <br/> Abstract. A homomorphism [math] from a guest graph [math] to a host graph [math] is locally bijective, injective, or surjective if for every [math], the restriction of [math] to the neighbourhood of [math] is bijective, injective, or surjective, respectively. We prove a number of new FPT (fixed-parameter tractable), W[1]-hard, and paraNP-complete results for the corresponding decision problems LBHom, LIHom, and LSHom by considering a hierarchy of parameters of the guest graph [math]. In this way we strengthen several existing results. For our FPT results, we develop a new algorithmic framework that involves a general ILP (integer linear program) model. We also use our framework to prove FPT results for the Role Assignment problem, which originates from social network theory and is closely related to locally surjective homomorphisms.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1285-1314, June 2024. Abstract. The voter model is a classical interacting particle system, modeling how global consensus is formed by local imitation. We analyze the time to consensus for a particular family of voter models when the underlying structure is a scale-free inhomogeneous random graph in the high edge–density regime, where this graph features a giant component. In this regime, we verify that the polynomial orders of consensus agree with those of their mean-field approximation in [A. Moinet, A. Barrat, and R. Pastor-Satorras, Phys. Rev. E, 98 (2018), 022303]. This “discursive” family of models has a symmetrized interaction to better model discussions and is indexed by a temperature parameter that, for certain parameters of the power law tail of the network’s degree distribution, is seen to produce two distinct phases of consensus speed. Our proofs rely on the well-known duality to coalescing random walks and a novel bound on the mixing time of these walks using the known fast mixing of the Erdős–Rényi giant subgraph. Unlike in the subcritical case [J. Fernley and M. Ortgiese, Random Structures Algorithms, 62 (2023), pp. 376–429], which requires tail exponent of the limiting degree distribution [math] as well as low edge density, in the giant component case, we also address the “ultrasmall world” power law exponents [math].
SIAM 离散数学杂志》第 38 卷第 2 期第 1285-1314 页，2024 年 6 月。 摘要投票者模型是一个经典的相互作用粒子系统，它模拟了全球共识是如何通过局部模仿形成的。我们分析了当底层结构是一个无标度的非均质随机图时，在高边沿密度系统中，一个特定的投票者模型族达成共识的时间。在这种情况下，我们验证了共识的多项式阶数与平均场近似 [A. Moinet, A. Barrat] 中的多项式阶数一致。Moinet, A. Barrat, and R. Pastor-Satorras, Phys. Rev. E, 98 (2018), 022303]。这个 "辨证 "模型系列有一个对称的相互作用，以更好地模拟讨论，并以一个温度参数为指标，对于网络度分布幂律尾的某些参数，可以看到共识速度会产生两个不同的阶段。我们的证明依赖于众所周知的凝聚随机游走的对偶性，以及利用已知的厄尔多斯-雷尼巨型子图的快速混合对这些游走的混合时间的新约束。与亚临界情况不同 [J. Fernley 和 M. Ort.Fernley 和 M. Ortgiese，Random Structures Algorithms，62 (2023)，pp. 376-429]需要极限度分布的尾指数[数学]以及低边缘密度，而在巨型分量情况下，我们还解决了 "超小世界 "幂律指数[数学]。
{"title":"Discursive Voter Models on the Supercritical Scale-Free Network","authors":"John Fernley","doi":"10.1137/22m1544373","DOIUrl":"https://doi.org/10.1137/22m1544373","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1285-1314, June 2024. <br/> Abstract. The voter model is a classical interacting particle system, modeling how global consensus is formed by local imitation. We analyze the time to consensus for a particular family of voter models when the underlying structure is a scale-free inhomogeneous random graph in the high edge–density regime, where this graph features a giant component. In this regime, we verify that the polynomial orders of consensus agree with those of their mean-field approximation in [A. Moinet, A. Barrat, and R. Pastor-Satorras, Phys. Rev. E, 98 (2018), 022303]. This “discursive” family of models has a symmetrized interaction to better model discussions and is indexed by a temperature parameter that, for certain parameters of the power law tail of the network’s degree distribution, is seen to produce two distinct phases of consensus speed. Our proofs rely on the well-known duality to coalescing random walks and a novel bound on the mixing time of these walks using the known fast mixing of the Erdős–Rényi giant subgraph. Unlike in the subcritical case [J. Fernley and M. Ortgiese, Random Structures Algorithms, 62 (2023), pp. 376–429], which requires tail exponent of the limiting degree distribution [math] as well as low edge density, in the giant component case, we also address the “ultrasmall world” power law exponents [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1269-1284, June 2024. Abstract. We prove that every family of (not necessarily distinct) even cycles [math] on some fixed [math]-vertex set has a rainbow even cycle (that is, a set of edges from distinct [math]’s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer [math].
{"title":"Rainbow Even Cycles","authors":"Zichao Dong, Zijian Xu","doi":"10.1137/23m1564808","DOIUrl":"https://doi.org/10.1137/23m1564808","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1269-1284, June 2024. <br/> Abstract. We prove that every family of (not necessarily distinct) even cycles [math] on some fixed [math]-vertex set has a rainbow even cycle (that is, a set of edges from distinct [math]’s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140562990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1250-1268, June 2024. Abstract. We completely characterize the triangulations of the projective plane that admit a spanning bipartite quadrangulation subgraph. This is an affirmative answer to a question by Kündgen and Ramamurthi [J. Combin. Theory Ser. B, 85 (2002), pp. 307–337] for the projective planar case.
{"title":"Spanning Bipartite Quadrangulations of Triangulations of the Projective Plane","authors":"Kenta Noguchi","doi":"10.1137/23m1566960","DOIUrl":"https://doi.org/10.1137/23m1566960","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1250-1268, June 2024. <br/> Abstract. We completely characterize the triangulations of the projective plane that admit a spanning bipartite quadrangulation subgraph. This is an affirmative answer to a question by Kündgen and Ramamurthi [J. Combin. Theory Ser. B, 85 (2002), pp. 307–337] for the projective planar case.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Natalie Behague, Tom Johnston, Shoham Letzter, Natasha Morrison, Shannon Ogden
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1239-1249, June 2024. Abstract. Given a graph [math], we say that an edge-colored graph [math] is [math]-rainbow saturated if it does not contain a rainbow copy of [math], but the addition of any nonedge in any color creates a rainbow copy of [math]. The rainbow saturation number [math] is the minimum number of edges among all [math]-rainbow saturated edge-colored graphs on [math] vertices. We prove that for any nonempty graph [math], the rainbow saturation number is linear in [math], thus proving a conjecture of Girão, Lewis, and Popielarz. In addition, we give an improved upper bound on the rainbow saturation number of the complete graph, disproving a second conjecture of Girão, Lewis, and Popielarz.
{"title":"The Rainbow Saturation Number Is Linear","authors":"Natalie Behague, Tom Johnston, Shoham Letzter, Natasha Morrison, Shannon Ogden","doi":"10.1137/23m1566881","DOIUrl":"https://doi.org/10.1137/23m1566881","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1239-1249, June 2024. <br/> Abstract. Given a graph [math], we say that an edge-colored graph [math] is [math]-rainbow saturated if it does not contain a rainbow copy of [math], but the addition of any nonedge in any color creates a rainbow copy of [math]. The rainbow saturation number [math] is the minimum number of edges among all [math]-rainbow saturated edge-colored graphs on [math] vertices. We prove that for any nonempty graph [math], the rainbow saturation number is linear in [math], thus proving a conjecture of Girão, Lewis, and Popielarz. In addition, we give an improved upper bound on the rainbow saturation number of the complete graph, disproving a second conjecture of Girão, Lewis, and Popielarz.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140562971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1222-1238, June 2024. Abstract. The determinant lower bound of Lovász, Spencer, and Vesztergombi [European J. Combin., 7 (1986), pp. 151–160] is a general way to prove lower bounds on the hereditary discrepancy of a set system. In their paper, Lovász, Spencer, and Vesztergombi asked if hereditary discrepancy can also be bounded from above by a function of the determinant lower bound. This was answered in the negative by Hoffman, and the largest known multiplicative gap between the two quantities for a set system of [math] subsets of a universe of size [math] is on the order of [math]. On the other hand, building upon work of Matoušek [Proc. Amer. Math. Soc., 141 (2013), pp. 451–460], Jiang and Reis [in Proceedings of the Symposium on Simplicity in Algorithms (SOSA), SIAM, Philadelphia, 2022, pp. 308–313] showed that this gap is always bounded up to constants by [math]. This is tight when [math] is polynomial in [math] but leaves open the case of large [math]. We show that the bound of Jiang and Reis is tight for nearly the entire range of [math]. Our proof amplifies the discrepancy lower bounds of a set system derived from the discrete Haar basis via Kronecker products.
SIAM 离散数学杂志》第 38 卷第 2 期第 1222-1238 页，2024 年 6 月。 摘要。Lovász、Spencer 和 Vesztergombi 的行列式下界 [European J. Combin., 7 (1986), pp.在他们的论文中，Lovász、Spencer 和 Vesztergombi 询问遗传差异是否也可以通过行列式下界的函数从上而下地限定。霍夫曼对此的回答是否定的，对于大小为[math]的宇宙的[math]子集的集合系统，这两个量之间已知的最大乘法差距是[math]数量级。另一方面，在马图塞克 [Proc. Amer. Math. Soc., 141 (2013), pp. 451-460] 的工作基础上，蒋和雷斯 [in Proceedings of the Symposium on Simplicity in Algorithms (SOSA), SIAM, Philadelphia, 2022, pp.当 [math] 是 [math] 的多项式时，这个界限很窄，但当 [math] 较大时，这个界限就很宽了。我们证明，几乎在 [math] 的整个范围内，Jiang 和 Reis 的约束都很紧。我们的证明扩大了通过克朗内克积从离散哈尔基导出的集合系统的差异下界。
{"title":"On the Gap Between Hereditary Discrepancy and the Determinant Lower Bound","authors":"Lily Li, Aleksandar Nikolov","doi":"10.1137/23m1566790","DOIUrl":"https://doi.org/10.1137/23m1566790","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1222-1238, June 2024. <br/> Abstract. The determinant lower bound of Lovász, Spencer, and Vesztergombi [European J. Combin., 7 (1986), pp. 151–160] is a general way to prove lower bounds on the hereditary discrepancy of a set system. In their paper, Lovász, Spencer, and Vesztergombi asked if hereditary discrepancy can also be bounded from above by a function of the determinant lower bound. This was answered in the negative by Hoffman, and the largest known multiplicative gap between the two quantities for a set system of [math] subsets of a universe of size [math] is on the order of [math]. On the other hand, building upon work of Matoušek [Proc. Amer. Math. Soc., 141 (2013), pp. 451–460], Jiang and Reis [in Proceedings of the Symposium on Simplicity in Algorithms (SOSA), SIAM, Philadelphia, 2022, pp. 308–313] showed that this gap is always bounded up to constants by [math]. This is tight when [math] is polynomial in [math] but leaves open the case of large [math]. We show that the bound of Jiang and Reis is tight for nearly the entire range of [math]. Our proof amplifies the discrepancy lower bounds of a set system derived from the discrete Haar basis via Kronecker products.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1202-1221, June 2024. Abstract. Let [math] be a bipartite graph where every node has a strict ranking of its neighbors. For any node, its preferences over neighbors extend naturally to preferences over matchings. A maximum matching [math] in [math] is a popular max-matching if there is no maximum matching more popular than [math]. In other words, for any maximum matching [math], the number of nodes that prefer [math] to [math] is at least the number of nodes that prefer [math] to [math]. It is known that popular max-matchings always exist in [math] and one such matching can be efficiently computed. In this paper we are in the weighted setting, i.e., there is a cost function [math], and our goal is to find a min-cost popular max-matching. We prove that such a matching can be computed in polynomial time by showing a compact extended formulation for the popular max-matching polytope. By contrast, it is known that the popular matching polytope has near-exponential extension complexity and finding a min-cost popular matching is NP-hard. We also consider Pareto-optimality. Though it is easy to find a Pareto-optimal matching/max-matching, we show that it is NP-hard to find a min-cost Pareto-optimal matching/max-matching.
{"title":"Maximum Matchings and Popularity","authors":"Telikepalli Kavitha","doi":"10.1137/22m1523248","DOIUrl":"https://doi.org/10.1137/22m1523248","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1202-1221, June 2024. <br/> Abstract. Let [math] be a bipartite graph where every node has a strict ranking of its neighbors. For any node, its preferences over neighbors extend naturally to preferences over matchings. A maximum matching [math] in [math] is a popular max-matching if there is no maximum matching more popular than [math]. In other words, for any maximum matching [math], the number of nodes that prefer [math] to [math] is at least the number of nodes that prefer [math] to [math]. It is known that popular max-matchings always exist in [math] and one such matching can be efficiently computed. In this paper we are in the weighted setting, i.e., there is a cost function [math], and our goal is to find a min-cost popular max-matching. We prove that such a matching can be computed in polynomial time by showing a compact extended formulation for the popular max-matching polytope. By contrast, it is known that the popular matching polytope has near-exponential extension complexity and finding a min-cost popular matching is NP-hard. We also consider Pareto-optimality. Though it is easy to find a Pareto-optimal matching/max-matching, we show that it is NP-hard to find a min-cost Pareto-optimal matching/max-matching.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1193-1201, June 2024. Abstract. Given a simple Eulerian binary matroid [math], what is the minimum number of disjoint circuits necessary to decompose [math]? We prove that [math] many circuits suffice if [math] is the complete binary matroid, for certain values of [math], and that [math] many circuits suffice for general [math]. We also determine the asymptotic behavior of the minimum number of circuits in an odd-cover of [math].
{"title":"Circuit Decompositions of Binary Matroids","authors":"Bryce Frederickson, Lukas Michel","doi":"10.1137/23m1587439","DOIUrl":"https://doi.org/10.1137/23m1587439","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1193-1201, June 2024. <br/> Abstract. Given a simple Eulerian binary matroid [math], what is the minimum number of disjoint circuits necessary to decompose [math]? We prove that [math] many circuits suffice if [math] is the complete binary matroid, for certain values of [math], and that [math] many circuits suffice for general [math]. We also determine the asymptotic behavior of the minimum number of circuits in an odd-cover of [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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