标准多重图中点不交的重边四边形  

Vertex-disjoint Multiquadrilaterals in Multigraphs

作　　者：石慧苓 高云澍 SHI Huiling;GAO Yunshu(School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia, 750021, P. R. China)

机构地区：[1]宁夏大学数学统计学院,银川宁夏750021

出　　处：《数学进展》2018年第3期348-362,共15页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11561054)

摘　　要：圈长为4的图叫做四边形,任意两个顶点之间边数至多为2的多重图叫做标准多重图,圈上的四条边都是重边的四边形叫重边四边形.本文证明了:如果M是阶数为4k的标准多重图,k是正整数,且M的最小度至少为6k-2,则除了三个特例之外,M包含k-1个重边四边形和一个有三条重边的四边形,使得这k个四边形彼此点不交.A cycle of length 4 is called a quadrilateral and a multigraph is called standard if every edge in it has multiplicity at most 2. A quadrilateral with four multiedges is called heavy-quadrilateral. We prove that if the minimum degree of M is at least 6 k-2, then M contains k vertex-disjoint quadrilaterals, such that k-1 of them are heavy-quadrilaterals and the remaining one is a quadrilateral with three multiedges, with only three exceptions.

关 键 词：重边四边形 标准多重图 最小度 

分 类 号：O157.5[理学—数学]