图中相互独立的4圈和含4个点的路

Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (6): 711-718.

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Quadrilaterals and Paths of Order 4 in Graphs

YAN Jin, LIU Gui-Zhen

山东大学数学与系统科学学院济南 250100

Online:2003-12-25 Published:2003-12-25
Supported by:
国家自然科学基金（60172003）和山东省自然科学基金（Z2000A02)资助项目

Abstract

Abstract:

Let k be a positive integer. Let G be a graph with |G|=4k. Supposeing σ\-2(G)≥4k-1, then G has a spanning subgra ph consisting of k-1quadrilaterals and a path of order 4 such that all of them are independent. Let G=(V\-1,V\-2;E) be a bipartite graph with |V\-1|=|V\-2|=2 k. If d(x)+d(y)≥2k+1 for each pair of nonadjacent vertices x and y of G with x∈V\-1and y∈V\-2, then G contains k-1 quadri laterals and a path of order 4 such that all of them are independent. Moreover,the condition on degrees is sharp.

Key words: Graph, Minimum degree, Cycle

CLC Number:

05C38，05C70

YAN Jin, LIU Gui-Zhen. Quadrilaterals and Paths of Order 4 in Graphs[J].Acta mathematica scientia,Series A, 2003, 23(6): 711-718.

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Quadrilaterals and Paths of Order 4 in Graphs

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