Pub Date : 2023-01-01DOI: 10.4236/ojdm.2023.133008
Junyu Luo, S. Ding
{"title":"Solving the <i>k</i>-Independent Sets Problem of Graphs by Gröbner Bases","authors":"Junyu Luo, S. Ding","doi":"10.4236/ojdm.2023.133008","DOIUrl":"https://doi.org/10.4236/ojdm.2023.133008","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/ojdm.2023.133007
Naoto Morikawa
{"title":"A Novel Design Method for Protein-Like Molecules from the Perspective of Sheaf Theory","authors":"Naoto Morikawa","doi":"10.4236/ojdm.2023.133007","DOIUrl":"https://doi.org/10.4236/ojdm.2023.133007","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/ojdm.2023.132005
Yanan Feng, Zhe Wang
{"title":"A Relationship between the Partial Bell Polynomials and Alternating Run Polynomials","authors":"Yanan Feng, Zhe Wang","doi":"10.4236/ojdm.2023.132005","DOIUrl":"https://doi.org/10.4236/ojdm.2023.132005","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-25DOI: 10.4236/ojdm.2023.131001
Russell Campbell, N. E. Clarke, G. MacGillivray
. Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.
{"title":"Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings","authors":"Russell Campbell, N. E. Clarke, G. MacGillivray","doi":"10.4236/ojdm.2023.131001","DOIUrl":"https://doi.org/10.4236/ojdm.2023.131001","url":null,"abstract":". Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41500608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-09DOI: 10.4236/ojdm.2022.123003
Lucas Freitas, Orlando Lee
Let $D$ be a digraph. A subset $S$ of $V(D)$ is a stable set if every pair of vertices in $S$ is non-adjacent in $D$. A collection of disjoint paths $mathcal{P}$ of $D$ is a path partition of $V(D)$, if every vertex in $V(D)$ is exactly on a path of $mathcal{P}$. We say that a stable set $S$ and a path partition $mathcal{P}$ are orthogonal if each path of $P$ contains exactly one vertex of $S$. A digraph $D$ satisfies the $alpha$-property if for every maximum stable set $S$ of $D$, there exists a path partition $mathcal{P}$ such that $S$ and $mathcal{P}$ are orthogonal. A digraph $D$ is $alpha$-diperfect if every induced subdigraph of $D$ satisfies the $alpha$-property. In 1982, Claude Berge proposed a characterization for $alpha$-diperfect digraphs in terms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee proposed a similar conjecture. A digraph $D$ satisfies the Begin-End-property or BE-property if for every maximum stable set $S$ of $D$, there exists a path partition $mathcal{P}$ such that (i) $S$ and $mathcal{P}$ are orthogonal and (ii) for each path $P in mathcal{P}$, either the start or the end of $P$ belongs to $S$. A digraph $D$ is BE-diperfect if every induced subdigraph of $D$ satisfies the BE-property. Sambinelli, Silva and Lee proposed a characterization for BE-diperfect digraphs in terms of forbidden blocking odd cycles. In this paper, we verified both conjectures for $3$-anti-circulant digraphs. We also present some structural results for $alpha$-diperfect and BE-diperfect digraphs.
{"title":"3-Anti-Circulant Digraphs Are <i>α</i>-Diperfect and BE-Diperfect","authors":"Lucas Freitas, Orlando Lee","doi":"10.4236/ojdm.2022.123003","DOIUrl":"https://doi.org/10.4236/ojdm.2022.123003","url":null,"abstract":"Let $D$ be a digraph. A subset $S$ of $V(D)$ is a stable set if every pair of vertices in $S$ is non-adjacent in $D$. A collection of disjoint paths $mathcal{P}$ of $D$ is a path partition of $V(D)$, if every vertex in $V(D)$ is exactly on a path of $mathcal{P}$. We say that a stable set $S$ and a path partition $mathcal{P}$ are orthogonal if each path of $P$ contains exactly one vertex of $S$. A digraph $D$ satisfies the $alpha$-property if for every maximum stable set $S$ of $D$, there exists a path partition $mathcal{P}$ such that $S$ and $mathcal{P}$ are orthogonal. A digraph $D$ is $alpha$-diperfect if every induced subdigraph of $D$ satisfies the $alpha$-property. In 1982, Claude Berge proposed a characterization for $alpha$-diperfect digraphs in terms of forbidden anti-directed odd cycles. In 2018, Sambinelli, Silva and Lee proposed a similar conjecture. A digraph $D$ satisfies the Begin-End-property or BE-property if for every maximum stable set $S$ of $D$, there exists a path partition $mathcal{P}$ such that (i) $S$ and $mathcal{P}$ are orthogonal and (ii) for each path $P in mathcal{P}$, either the start or the end of $P$ belongs to $S$. A digraph $D$ is BE-diperfect if every induced subdigraph of $D$ satisfies the BE-property. Sambinelli, Silva and Lee proposed a characterization for BE-diperfect digraphs in terms of forbidden blocking odd cycles. In this paper, we verified both conjectures for $3$-anti-circulant digraphs. We also present some structural results for $alpha$-diperfect and BE-diperfect digraphs.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46457331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4236/ojdm.2022.121001
M. Huilgol, B. Divya
{"title":"Geodetic Number and Geo-Chromatic Number of 2-Cartesian Product of Some Graphs","authors":"M. Huilgol, B. Divya","doi":"10.4236/ojdm.2022.121001","DOIUrl":"https://doi.org/10.4236/ojdm.2022.121001","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4236/ojdm.2022.124007
M. Beatriz
{"title":"Restabilization Process in Matching Markets with Workers Proposing","authors":"M. Beatriz","doi":"10.4236/ojdm.2022.124007","DOIUrl":"https://doi.org/10.4236/ojdm.2022.124007","url":null,"abstract":"","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70627762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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