偶匹配可扩性的极图问题(英文)

Extremal Graphs about Bipartite Matching Extendability

设G是含有完美匹配的简单图.称图G是偶匹配可扩的(BM-可扩的),如果G的每一个导出子图是偶图的匹配M都可以扩充为一个完美匹配.极图问题是图论的核心问题之一.本文将刻画极大偶匹配不可扩图,偶图图类和完全多部图图类中的极大偶匹配可扩图.

Let G be a simple graph containing a perfect matching. G is said to be bipartite matching extendable （BM-extendable） if every matching M whose induced subgraph is a bipartite graph extends to a perfect matching. Extremal graph problems are at the core of graph theory. In this paper, we characterize maximally BM-unextendable graphs, maximally BM-extendable graphs in the class of complete k-partite graphs with k≥2.