4连通1-平面弦图是哈密顿连通的

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-04-18 DOI:10.1002/jgt.23250

Licheng Zhang, Yuanqiu Huang, Shengxiang Lv, Fengming Dong

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引用次数: 0

摘要

Tutte证明了4连通平面图是哈密顿图。在1-平面图上是否有类似的结果是未知的。本文刻画了4连通1平面弦图，并证明了所有这些弦图都是哈密顿连通的。在我们的证明中使用的一个关键工具是1-平面4-树的特性。

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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4-Connected 1-Planar Chordal Graphs Are Hamiltonian-Connected

Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar chordal graphs and show that all such graphs are Hamiltonian-connected. A crucial tool used in our proof is a characteristic of 1-planar 4-trees.

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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 .