Pub Date : 2023-03-08DOI: 10.1007/978-3-031-06678-8_5
Bogdan Alecu, V. E. Alekseev, A. Atminas, V. Lozin, V. Zamaraev
{"title":"Graph Parameters, Implicit Representations and Factorial Properties","authors":"Bogdan Alecu, V. E. Alekseev, A. Atminas, V. Lozin, V. Zamaraev","doi":"10.1007/978-3-031-06678-8_5","DOIUrl":"https://doi.org/10.1007/978-3-031-06678-8_5","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88214647","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}
Valentin Bartier, N. Bousquet, Carl Feghali, Marc Heinrich, B. Moore, Théo Pierron
{"title":"Recoloring Planar Graphs of Girth at Least Five","authors":"Valentin Bartier, N. Bousquet, Carl Feghali, Marc Heinrich, B. Moore, Théo Pierron","doi":"10.1137/21m1463598","DOIUrl":"https://doi.org/10.1137/21m1463598","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72930481","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 : 2023-02-07DOI: 10.1137/1.9781611975062.15
Kunal Dutta, C. Subramanian
We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path chromatic number and tree chromatic number i.e. the smallest number of parts into which the vertex set of a graph can be partitioned such that every The arguments involve the application of a modified version of a probabilistic inequality of Krivelevich, Sudakov, Vu and Wormald.
{"title":"On Induced Paths, Holes and Trees in Random Graphs","authors":"Kunal Dutta, C. Subramanian","doi":"10.1137/1.9781611975062.15","DOIUrl":"https://doi.org/10.1137/1.9781611975062.15","url":null,"abstract":"We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path chromatic number and tree chromatic number i.e. the smallest number of parts into which the vertex set of a graph can be partitioned such that every The arguments involve the application of a modified version of a probabilistic inequality of Krivelevich, Sudakov, Vu and Wormald.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75960188","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}
{"title":"Disjoint Cycles in a Digraph with Partial Degree","authors":"Hong Wang, Yun Wang, Jin Yan","doi":"10.1137/21m1460594","DOIUrl":"https://doi.org/10.1137/21m1460594","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90857384","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}
{"title":"A New Bound for Hadwiger's Covering Problem in (boldsymbol{mathbb{E}}^3)","authors":"A. Prymak","doi":"10.1137/22m1490314","DOIUrl":"https://doi.org/10.1137/22m1490314","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79743188","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: 10.48550/arXiv.2206.13810
M. Shi, Xuan Wang
{"title":"Gray Images of Cyclic Codes over Zp2 and ZpZp2","authors":"M. Shi, Xuan Wang","doi":"10.48550/arXiv.2206.13810","DOIUrl":"https://doi.org/10.48550/arXiv.2206.13810","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76941072","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}
Frantisek Kardos, Jonathan Narboni, R. Naserasr, Zhouningxin Wang
{"title":"Circular ({boldsymbol{(4-epsilon )}}) -Coloring of Some Classes of Signed Graphs","authors":"Frantisek Kardos, Jonathan Narboni, R. Naserasr, Zhouningxin Wang","doi":"10.1137/21m1436257","DOIUrl":"https://doi.org/10.1137/21m1436257","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90630287","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 : 2022-11-28DOI: 10.48550/arXiv.2211.15350
Yanhui Zhang
BCH codes are an important class of cyclic codes, and have wide applicantions in communication and storage systems. However, it is difficult to determine the parameters of BCH codes and only a few cases are known. In this paper, we mainly study three classes of BCH codes with $n=q^{m}-1,frac{q^{2s}-1}{q+1},frac{q^{m}-1}{q-1}$. On one hand, we accurately give the parameters of $mathcal C_{(q,n,delta,1)}$ and its dual codes. On the other hand, we give the sufficient and necessary conditions for $mathcal C_{(q,n,delta,2)}$ being dually-BCH codes.
{"title":"Three classes of BCH codes and their duals","authors":"Yanhui Zhang","doi":"10.48550/arXiv.2211.15350","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15350","url":null,"abstract":"BCH codes are an important class of cyclic codes, and have wide applicantions in communication and storage systems. However, it is difficult to determine the parameters of BCH codes and only a few cases are known. In this paper, we mainly study three classes of BCH codes with $n=q^{m}-1,frac{q^{2s}-1}{q+1},frac{q^{m}-1}{q-1}$. On one hand, we accurately give the parameters of $mathcal C_{(q,n,delta,1)}$ and its dual codes. On the other hand, we give the sufficient and necessary conditions for $mathcal C_{(q,n,delta,2)}$ being dually-BCH codes.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78314878","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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