平方树中的Pk-因子OA
Pk-Factors in the Squares of Trees
如果H是图G的一个生成子图,并且H的每个连通分支都是包含k个顶点的路,则称生成子图H是图G的一个Pk-因子.图G的平方图G2 的顶点集为V(G),且在G2 中两顶点相邻当且仅当这两顶点在图G中距离小于等于2.文中主要研究了图的Pk-因子问题,通过树的特殊结构刻画了一些图的参数之间的关系,得到了在树的平方图中存在Pk-因子的一个必要条件.最后,构造了两类满足结论中不等式取等的无穷图类.
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.
冯星;李佳林
集美大学理学院,福建 厦门 361021集美大学理学院,福建 厦门 361021
数理科学
图路径因子Pk-因子树平方图
graphpath factorPk-factortreesquare graph
《集美大学学报（自然科学版）》 2026 (1)
121-126,6
福建省自然科学基金项目(2023J05164)
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