集美大学学报（自然科学版）2026，Vol.31Issue(1)：121-126,6.DOI:10.19715/j.jmuzr.2026.01.12
平方树中的Pk-因子
Pk-Factors in the Squares of Trees
摘要
Abstract
A spanning subgraph H of G is a Pk-factor if each component of H is a path of k vertices.The square of a graph G,denoted by G2,is the graph with vertex set V(G)such that two vertices are adjacent in G2 if and only if their distance in G is at most 2.In this paper,we investigate the Pk-factor problem in graphs.By the special structure of the tree,this paper characterizes the relationships between some graph parameters and obtains a necessary condition for the existence of the Pk-factors in squares of trees.Finally,this paper con-structs two infinite families of graphs that satisfy the equality condition in the conclusion's inequalities.关键词
图/路径因子/Pk-因子/树/平方图Key words
graph/path factor/Pk-factor/tree/square graph分类
数理科学引用本文复制引用
冯星,李佳林..平方树中的Pk-因子[J].集美大学学报（自然科学版）,2026,31(1):121-126,6.基金项目
福建省自然科学基金项目(2023J05164) （2023J05164）
