VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

Jin YAN;Gui Zhen LIU

Journal of Systems Science & Complexity ›› 2004, Vol. 14 ›› Issue (4) : 532-537.

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PDF(101 KB)
Journal of Systems Science & Complexity ›› 2004, Vol. 14 ›› Issue (4) : 532-537.
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VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

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Abstract

H. Wang considered the minimum degrees condition that G has large vertex-disjoint 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 m3, n2 and k1 be three integers. Let G=(V1,V2;E) be a bipartite graph with |V1|=|V2|=n2k+1. If the minimum degree δ(G)k+1 and xV(C)d(x)m(n+1)+1 for any cycle C of G with length 2m, then G contains k vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp.

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Graphs / bipartite graphs / quadrilaterals / cycles

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Jin YAN , Gui Zhen LIU. VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS. Journal of Systems Science and Complexity, 2004, 14(4): 532-537
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