太阳图与路的笛卡儿积图的任意可分性  

Partitioning the Cartesian Product of a Sun-like Graph and a Path

作　　者：西日尼阿依·努尔麦麦提 刘凤霞[1] 孟吉翔[1] Xirinay NURMAMAT;LIU Fengxia;MENG Jixiang(College of Mathematics and Systems Science,Xinjiang University,Urumqi,Xinjiang,830046,P.R.China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学进展》2022年第1期32-40,共9页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11501487;11961067 and 11531011)。

摘　　要：一个阶为n的图G称为是任意可分的(简作AP),如果对于任一正整数序列τ=(n_(1),n_(2),…,n_(k))满足n=n_(1)+n_(2)+…+n_(k),总是存在顶点集V(G)的一个划分(V_(1),V_(2),…,V_(k))满足:对于i∈[1,k],|V_(i)|=n_(i),且子图G|V_(i)|是图G的V_(i)导出的一个连通子图.我们用S^(*)=S(n;m_(1),m_(2),…,m_(n))来表示最大度△(S^(*))=3的太阳图.本文讨论了图S^(*)P_(m)(m≥3)的任意可分性.A graph G of order n is called arbitrarily partitionable(AP for short)if for any sequenceτ=(n1,n2,…,nk)of positive integers such that n=n1+n2+…+nk,there exists a partition(V_(1),V_(2),…Vk)of the vertex set of V(G)such that|V_(i)|=ni and subgraph G[V_(i)]induced by V_(i) is connected in G for i∈[1,k].We use S*=S(n;m1,m2,…,mn)to denote the sun-like graph of maximum degreeΔ(S*)=3.In this paper,we discuss the arbitrary partitionability of graph S*□Pm(m≥3).

关 键 词：任意可分图 图的笛卡儿积 太阳图 可迹的 

分 类 号：O157.5[理学—数学]