Finding triangle-free 2-factors in general graphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-03-08 DOI:10.1002/jgt.23089

David Hartvigsen

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引用次数: 0

Abstract

A 2-factor in a graph $G$ is a subset of edges $M$ such that every node of $G$ is incident with exactly two edges of $M$ . Many results are known concerning 2-factors including a polynomial-time algorithm for finding 2-factors and a characterization of those graphs that have a 2-factor. The problem of finding a 2-factor in a graph is a relaxation of the NP-hard problem of finding a Hamilton cycle. A stronger relaxation is the problem of finding a triangle-free 2-factor, that is, a 2-factor whose edges induce no cycle of length 3. In this paper, we present a polynomial-time algorithm for the problem of finding a triangle-free 2-factor as well as a characterization of the graphs that have such a 2-factor and related min–max and augmenting path theorems.

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在一般图形中寻找无三角形的 2 因子

图 G$G$ 中的 2 因子是边 M$M$ 的一个子集，使得 G$G$ 的每个节点都正好与 M$M$ 的两条边相连。有关 2 因子的许多结果已经为人所知，其中包括寻找 2 因子的多项式时间算法和具有 2 因子的图的特征描述。在图中寻找 2 因子的问题是寻找汉密尔顿循环这一 NP 难问题的松弛。本文提出了寻找无三角形 2 因子问题的多项式时间算法，以及具有这种 2 因子的图的特征和相关的最小-最大和增强路径定理。

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

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .