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VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

YanJin、LIUGuizhen

2004系统科学与复杂性：英文版Mathematics被引 3

摘要

H.Wang considered the minimum degrees condition that G has large vertexdisjoint cycles in bipartite graphs.Motivated by this,we consider the small vertex-disjoint cycles in bipartite graphs in this paper.We prove the following result:Let m≥3,n≥2 and k≥1 be three integers.Let G=(V1,V2;E)be a bipartite graph with |V1|=|V2|=n≥2k+1.If the minimum degree δ(G)≥k+1and x∈V(C)^∑d(x)≥m(n+1)+1 for any cycle C of G with length 2m,then Gcontains k vertex-disjoint cycles of length 4.Moreover,the degrees condition is sharp.

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