文献类型：期刊文献

英文题名：Spectral conditions for k-extendability and k-factors of bipartite graphs

作者：Fan, Dandan[1,2]; Lin, Huiqiu[1]

机构：[1] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China; [2] College of Mathematics and Physics, Xinjiang Agricultural University, Urumqi, Xinjiang, 830052, China

年份：2022

外文期刊名：arXiv

收录：EI(收录号：20220429470)

语种：英文

外文关键词：Graph theory

摘要：Let G be a connected graph. If G contains a matching of size k, and every matching of size k is contained in a perfect matching of G, then G is said to be k-extendable. A k-regular spanning subgraph of G is called a k-factor. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree δ to be k-extendable, and for the existence of a k-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in [10] and [25] to k-extendable graphs. Furthermore, our results generalize the result of Lu, Liu and Tian [22] to general regular factors. Additionally, using the equivalence of k edge-disjoint perfect matchings and k-factors in balanced bipartite graphs, our results can derive a spectral condition for the existence of k edge-disjoint perfect matchings in balanced bipartite graphs. ? 2022, CC BY.