Non-Hamiltonian Cartesian products of two even dicycles

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Graph Theory Pub Date : 2024-09-30 DOI:10.1002/jgt.23185

Kenta Noguchi, Carol T. Zamfirescu

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引用次数: 0

Abstract

In this note it is proven that there exist infinitely many positive integers $a$ and $b$ such that the Cartesian product of a directed cycle of length $2 a$ and a directed cycle of length $2 b$ is non-Hamiltonian. In particular, the Cartesian product of an 880-dicycle and a 4368-dicycle is non-Hamiltonian. We also prove that there is no such graph on fewer than $880 \cdot 4368 = 3, 843, 840$ vertices, which is rather astonishing.

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本论文证明了存在无穷多个正整数 a $a$ 和 b $b$ ，使得长度为 2 a $2a$ 的有向循环和长度为 2 b $2b$ 的有向循环的笛卡儿积为非哈密尔顿积。特别是，880-圆周和 4368-圆周的笛卡儿积为非哈密尔顿积。我们还证明了在少于 880 ⋅ 4368 = 3 , 843 , 840 $880\cdot 4368=3,843,840$ 的顶点上不存在这样的图，这是相当惊人的。

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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 .

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Issue Information Issue Information Issue Information Counting circuit double covers Non-Hamiltonian Cartesian products of two even dicycles