Some Existence Theorems on Path Factors with Given Properties in Graphs  

作　　者：Si Zhong ZHOU Zhi Ren SUN 

机构地区：[1]School of Science,Jiangsu University of Science and Technology,Zhenjiang 212003,P.R.China [2]School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第8期917-928,共12页数学学报（英文版）

基　　金：Supported by Six Big Talent Peak of Jiangsu Province(Grant No.JY–022);333 Project of Jiangsu Province;the National Natural Science Foundation of China(Grant No.11371009)。

摘　　要：A path factor of G is a spanning subgraph of G such that its each component is a path.A path factor is called a P≥n-factor if its each component admits at least n vertices.A graph G is called P≥n-factor covered if G admits a P≥n-factor containing e for any e∈E(G),which is defined by[Discrete Mathematics,309,2067-2076(2009)].We first define the concept of a(P≥n,k)-factor-critical covered graph,namely,a graph G is called(P≥n,k)-factor-critical covered if G-D is P≥n-factor covered for any D⊆V(G)with|D|=k.In this paper,we verify that(i)a graph G withκ(G)≥k+1 is(P≥2,k)-factor-critical covered if bind(G)>2+k/3;(ii)a graph G with|V(G)|≥k+3 andκ(G)≥k+1 is(P≥3,k)-factor-critical covered if bind(G)≥4+k/3.

关 键 词：GRAPH binding number P≥2-factor P≥3-factor (P≥2 k)-factor-critical covered graph (P≥3 k)-factor-critical covered graph 

分 类 号：O157.5[理学—数学]