Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2023-12-19 DOI:10.1007/s00493-023-00078-9

Yulai Ma, Davide Mattiolo, Eckhard Steffen, Isaak H. Wolf

引用次数: 0

Abstract

For \(0 \le t \le r\) let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance \(m(3,3)=m(4,r)=1\), and \(m(t,r) \le r-2\) for all \(t \not = 5\), and \(m(t,r) \le r-3\) if r is even. We prove that \(m(2l,r) \le 3l - 6\) for every \(l \ge 3\) and \(r \ge 2 l\).

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正则图中的边连接性和成对不相交完全匹配

对于（0 \le t \le r\），让 m(t, r) 是最大的数 s，使得每个 t 边连接的 r 图都有 s 个成双成对的完美匹配。m(t,r)只有少数几个已知值，例如：（m(3,3)=m(4,r)=1），在所有（t不=5）的情况下（m(t,r) （le r-2），如果r是偶数，则（m(t,r) （le r-3）。我们证明，对于每一个l和r来说，m（2l,r）都是3l-6。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.