摘要
若多重二部图中不同划分的任意一对点之间至多包含两条边,则称其为标准多重二部图.令D是一个标准多重二部图,使得|V_(1)|=|V_(2)|=n≥2,其中n是正整数.我们证明了若D的最小度至少是3n/2,则D一定包含[n/2]个点不交的4圈,并且当n为奇数时,上述n/2个4圈中的前n-3/2中的每条边都是重边,剩余的一个4圈中至少有3条边是重边;当n为偶数时,前n-4/2个4圈的每条边都是重边,剩余的两个4圈中每个至少有3条边是重边,除非有一个例外.
A bipartite multigraph is called a standard bipartite multigraph if each edge in it contains at least two edges.Let D be a standard bipartite multigraph with|V_(1)|=|V_(2)|=n≥2,where n is a positive integer.We prove that if the minimum degree of D is at least 3n/2,then D contains[n/2]vertex-disjoint quadrilatearls.Moreover,if n is odd,then n-2/3 of[n/2]disjoint quadrilaterals has four multiedges and the rest one of them has at least three multiedges;if n is even,then n-2/4 of[n/2]disjoint quadrilaterals has four multiedges and each of the rest of two has at least three multiedges,with only one exception.
作者
王雪
高云澍
WAGNG Xue;GAO Yunshu(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)
出处
《应用数学学报》
CSCD
北大核心
2021年第3期383-392,共10页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(12061056,11561054)
宁夏自然科学基金(2021AAC05001)
宁夏回族自治区青年拔尖人才资助项目。
关键词
标准多重二部图
点不交
4圈
standard bipartite multigraph
vertex-disjoint
quadrilaterals