Clique Numbers of Graphs and Irreducible Exact m-Covers of Z

dc.creatorPan, Hao
dc.creatorZhao, Li-Lu
dc.date2008-04-06
dc.date2008-04-26
dc.date.accessioned2026-07-07T09:35:07Z
dc.date.available2026-07-07T09:35:07Z
dc.descriptionFor each m>=1 and k>=2, we construct a graph G=(V,E) with ω(G)=m such that max_{1\leq i\leq k} ω(G[V_i])=m for arbitrary partition V=V_1\cup...\cup V_k, where ω(G) is the clique number of G and G[V_i] is the induced subgraph of G with the vertex set V_i. Using this result, we show that for each m>=2 there exists an exact m-cover of Z which is not the union of two 1-covers.
dc.description7 pages. Conjecture 3.1 in the first version has been solved
dc.identifierhttps://arxiv.org/abs/0804.0901
dc.identifierhttp://arxiv.org/abs/0804.0901
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159729
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject05C30 (Primary); 11B25, 05C90, 05C20(Secondary)
dc.titleClique Numbers of Graphs and Irreducible Exact m-Covers of Z
dc.typetext

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