Spanning even trees of graphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-05-08 DOI:10.1002/jgt.23115

Bill Jackson, Kiyoshi Yoshimoto

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引用次数: 0

Abstract

A tree $T$ is said to be even if all pairs of vertices of degree one in $T$ are joined by a path of even length. We conjecture that every $r$ -regular nonbipartite connected graph $G$ has a spanning even tree and verify this conjecture when $G$ has a 2-factor. Well-known results of Petersen and Hanson et al. imply that the only remaining unsolved case is when $r$ is odd and $G$ has at least $r$ bridges. We investigate this case further and propose some related conjectures.

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图的跨偶数树

如果所有阶数为 1 的顶点对都由一条长度为偶数的路径连接，则称该树为偶数树。我们猜想，每一个-规则的非双方形连通图都有一棵跨度为偶数的树，并在有 2 因子时验证了这一猜想。Petersen 和 Hanson 等人的著名结果意味着，唯一剩下的未解情况是奇数且至少有桥。我们将进一步研究这种情况，并提出一些相关猜想。

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 .