An Ore-type condition for large k-factor and disjoint perfect matchings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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An Ore-type condition for large k-factor and disjoint perfect matchings

Authors:	Hongliang Lu Bo Ning

Institution:	1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China;2. Center for Applied Mathematics, Tianjin University, Tianjin, China

Abstract:	Win conjectured that a graph $G$ on $n$ vertices contains $k$ disjoint perfect matchings, if the degree sum of any two nonadjacent vertices is at least $n + k - 2$ , where $n$ is even and $n \geq k + 2$ . In this paper, we prove that Win's conjecture is true for $k \geq n ∕ 2$ , where $n$ is sufficiently large. To show this result, we prove a theorem on $k$ -factor in a graph under some Ore-type condition. Our main tools include Tutte's $k$ -factor theorem, the Karush-Kuhn-Tucker theorem on convex optimization and the solution to the long-standing 1-factor decomposition conjecture.

Keywords:	degree sum factorization hamiltonian graph Karush-Kuhn-Tucker condition Ore-type condition perfect matching regular graph