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Odd covers of graphs

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dc.contributor.authorBuchanan, Calum-
dc.contributor.authorAlexander Clifton-
dc.contributor.authorCulver, Eric-
dc.contributor.authorNie, Jiaxi-
dc.contributor.authorO'Neill, Jason-
dc.contributor.authorRombach, Puck-
dc.contributor.authorYin, Mei-
dc.date.accessioned2023-09-13T22:01:56Z-
dc.date.available2023-09-13T22:01:56Z-
dc.date.created2023-05-24-
dc.date.issued2023-05-
dc.identifier.issn0364-9024-
dc.identifier.urihttps://pr.ibs.re.kr/handle/8788114/13921-
dc.description.abstractGiven a finite simple graph G $G$, an odd cover of G $G$ is a collection of complete bipartite graphs, or bicliques, in which each edge of G $G$ appears in an odd number of bicliques, and each nonedge of G $G$ appears in an even number of bicliques. We denote the minimum cardinality of an odd cover of G $G$ by b2(G) ${b}_{2}(G)$ and prove that b2(G) ${b}_{2}(G)$ is bounded below by half of the rank over F2 ${{\mathbb{F}}}_{2}$ of the adjacency matrix of G $G$. We show that this lower bound is tight in the case when G $G$ is a bipartite graph and almost tight when G $G$ is an odd cycle. However, we also present an infinite family of graphs which shows that this lower bound can be arbitrarily far away from b2(G) ${b}_{2}(G)$. Babai and Frankl proposed the "odd cover problem," which in our language is equivalent to determining b2(Kn) ${b}_{2}({K}_{n})$. In this paper, we determine that b2(Kn) ${b}_{2}({K}_{n})$ is n/2 $n\unicode{x02215}2$ when 8 divide n $8| n$ and is (n+1)/2 $(n+1)\unicode{x02215}2$ when n $n$ is equivalent to 1 or -1 $-1$ modulo 8.-
dc.language영어-
dc.publisherWILEY-
dc.titleOdd covers of graphs-
dc.typeArticle-
dc.type.rimsART-
dc.identifier.wosid000981508000001-
dc.identifier.scopusid2-s2.0-85158171896-
dc.identifier.rimsid80832-
dc.contributor.affiliatedAuthorAlexander Clifton-
dc.identifier.doi10.1002/jgt.22970-
dc.identifier.bibliographicCitationJOURNAL OF GRAPH THEORY, v.104, no.2, pp.420 - 439-
dc.relation.isPartOfJOURNAL OF GRAPH THEORY-
dc.citation.titleJOURNAL OF GRAPH THEORY-
dc.citation.volume104-
dc.citation.number2-
dc.citation.startPage420-
dc.citation.endPage439-
dc.type.docTypeArticle; Early Access-
dc.description.journalClass1-
dc.description.journalClass1-
dc.description.isOpenAccessN-
dc.description.journalRegisteredClassscie-
dc.description.journalRegisteredClassscopus-
dc.relation.journalResearchAreaMathematics-
dc.relation.journalWebOfScienceCategoryMathematics-
dc.subject.keywordAuthorbipartite subgraph complementation-
dc.subject.keywordAuthorcomplete bipartite graph-
dc.subject.keywordAuthorGraham-Pollak-
dc.subject.keywordAuthorodd cover problem-
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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