Some New Results Of Matching Extendable Graphs

Matching theory is at the core of graph theory. Since it has importantapplications and is in connection with other theoretic problems closely, ithas been studied extensively. And many celebrated results have been es-tablished, such as Hall's theorem and Tutte's theorem, characterizing thosegraphs with perfect matchings; Gallai-Edmords structure theorem, and so on.In the meantime, many typical topics arise, matching extendability(includingk-extendability, Induced-Matching extendability, and Bipartite-Matching ex-tendability)is one of them.Note that there is a close relation in Matching extendability:k-extendable (k = m(G)) (?) Bipartite-Matchingextendable (?) Induced-Matching extendable (?) 1-extendable (?) elementary,where m(G) is the cardinality of a maximun matching of G.Graphs considered in this thesis are finite, undirected and simple. Thisthesis consists three chapters.In charpter1, we introduce the background of our study and some notations.Finally, we introduce studying contents and main results in this paper.In charpter2, we first study the property of Induced-Matching extendablegraphs. Then we study the Fan's condition, Degree sum and connectivityconditions of Induced-Matching extendable graphs.In charpter3, we study the Fan's condition, Degree sum and connectivityconditions of Bipartite-Matching extendable graphs.