K 1,3 -Free图上的弦泛圈性  

Chorded Pancyclicity on K 1,3 -Free Graph

作　　者：李欢 田增娴 杨卫华 

机构地区：[1]太原理工大学数学学院,山西 太原 [2]成都信息工程大学应用数学学院,四川 成都

出　　处：《应用数学进展》2024年第5期1994-1999,共6页Advances in Applied Mathematics

摘　　要：一个非诱导圈被称为弦圈,即在图中至少有一条额外的边连接圈内两个非相邻的顶点。一个阶数为n的图G, 如果G包含长度为从4到n的弦圈,则称为弦泛圈图。1991年,R.J. Faudree, R.J. Gould和T.E. Lindquester得出结论:令G是阶数为n(n≥14)的2-连通,K1,3-free图。如果对于每一对不相邻的顶点x,y,有|N(x)∪N(y)|≥2n−23,则G是泛圈图。在本文中,我们扩展了这个结果,把泛圈性推广到弦泛圈性:对于任意2-连通,阶数为n(n≥34)的K1,3-free图G,如果每对不相邻顶点x,y∈V(G),满足|N(x)∪N(y)|≥2n−23,则图G是弦泛圈图。A non-induced cycle is called a chorded cycle, that is, a cycle that has at least one additional edge connecting two non-consecutive vertices within the cycle. A graph G of order n is chorded pancyclic if G contains a chorded cycle of each length from 4 to n. In 1991, R.J. Faudree, R.J. Gould, and T.E. Lindquester concluded: Let G be a 2-connectedK1,3-free graph with the ordern(n≥14). If|N(x)∪N(y)|≥2n−23for each pair of nonadjacent verticesx,y, then G is pancyclic. In this paper, we extended this result by generalizing the concept of pancyclicto chorded pancyclic: ever 2-connected,K1,3-free graph G with ordern≥43is chorded pancyclic if the number of the union of for each pair of nonadjacent vertices at least2n−23.

关 键 词：-Free 弦圈 泛圈 弦泛圈 哈密尔顿 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]