分数(g,f,m)-消去图的不相邻顶点领域并条件

数学理论与应用 ›› 2016, Vol. 36 ›› Issue (4): 36-43.

分数(g,f,m)-消去图的不相邻顶点领域并条件

钟结枚¹ ，高炜²

1.云南师范大学数学学院,昆明,650500; 2.云南师范大学信息学院,昆明,650500

出版日期:2016-12-30 发布日期:2020-09-25
基金资助:
国家自然科学基金项目(no.11401519)资助

Non-adjacent Vertices Neighborhood Union Condition for Fractional(g,f,m)-deleted Graphs

Zhong Jiemei¹ ，Gao Wei ²

1.School of Mathematics,Yunnan Normal University,Kunming 650500,China; 2.School of Information Science and Technology,Yunnan Normal University,Kunming 650500,China

Online:2016-12-30 Published:2020-09-25

摘要/Abstract

摘要：

一个图称为分数(g,f,m)-消去图若删除任意m 条边后的剩余子图依然存在分数(g,f)-因子.本文证明若图G 的阶为n,1≤a ≤g(x)≤f(x)-Δ ≤b-Δ 对任意顶点x ∈V(G)成立,δ(G)≥ (b-Δ)(b+1)/a+2m,n≥(a+b)(2(a+b)+2m-1)/(a+Δ), 且|NG(x1)∪NG(x2)|≥(b-Δ)n/(a+b)对任意不相邻顶点x1和x2都成立,则G 是分数(g,f,m)-消去图.这个领域并条件在一定程度上是最好的.

关键词: 图, 领域并条件, 分数消去图

Abstract: A graph G is called a fractional(g,f,m)-deleted graph if the resulting graph admits a fractional(g,f)-factor after any medges are deleted.In this paper,we prove that if Gis a graph of order n,1≤a ≤g(x)≤f(x)-Δ≤b-Δ for any x∈V(G),δ(G)≥(b-Δ)(b+1)/a+2m,n≥(a+b)(2(a+b)+2m-1)/(a+Δ), and|NG(x1)∪NG(x2)|≥(b-Δ)n/(a+b) for any non-adjacent vertices x1 and x2,then G is a fractional(g,f,m)-deleted graph.The result is tight on the neighborhood union condition in some sense

Key words: Graph, Neighborhood union condition, Fractional deleted graph

钟结枚, 高炜. 分数(g,f,m)-消去图的不相邻顶点领域并条件[J]. 数学理论与应用, 2016, 36(4): 36-43.

Zhong Jiemei , Gao Wei .

Non-adjacent Vertices Neighborhood Union Condition for Fractional(g,f,m)-deleted Graphs [J]. Mathematical Theory and Applications, 2016, 36(4): 36-43.