哈林图的匹配可扩性研究

Study on the Matching Extendibility of HalinGraphsAbstractMatching theory is the core of graph theory,and it is also a research fieldfull of vitality.Its application background is very wide,involving a large numberof theoretical problems.These theories have a strong influence in graph theory,and the matching extensibility is one of the research topics in a series of emergingrelated to the matching theory.In this paper,we study the k-extendibility,induced-matching extendability,and Bipartite-Matching extendability of Halin graphs.This paper first describesthe generation and development process of matching theory,and then summarizesthe research results of matching extendibility at home and abroad.This paperanalyzes the k-extendibility,induced-matching extendability and bipartite-matching extendability of a Halin graph.It is concluded that a Halin graph G isonly 1-extendable;Halin graph G is IM-extendable if and only if its characteristictree Tis isomorphic to K3,Ks,K or S2;Halin graph Gis BM-extendableif and only if its characteristic tree T is isomorphic to K13,Ki.s,K.7.Keywords:Halin graph;k-extendable;Induced-Matching extendable;Bipartite-Matching extendable