A characterization of regular partial cubes whose all convex cycles have the same lengths

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-06-28 DOI:10.1002/jgt.23126

Yan-Ting Xie, Yong-De Feng, Shou-Jun Xu

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引用次数: 0

Abstract

Partial cubes are graphs that can be isometrically embedded into hypercubes. Convex cycles play an important role in the study of partial cubes. In this paper, we prove that a regular partial cube is a hypercube (resp., a Doubled Odd graph, an even cycle of length $2 n$ where $n ⩾ 4$ ) if and only if all its convex cycles are 4-cycles (resp., 6-cycles, $2 n$ -cycles). In particular, the partial cubes whose all convex cycles are 4-cycles are equivalent to almost-median graphs. Therefore, we conclude that regular almost-median graphs are exactly hypercubes, which generalizes the result by Mulder—regular median graphs are hypercubes.

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所有凸循环长度相同的规则局部立方体的特征描述

部分立方体是可以等距嵌入超立方体的图形。凸周期在部分立方体的研究中发挥着重要作用。本文证明，当且仅当一个规则部分立方体的所有凸循环都是 4 循环（或 6 循环、-循环）时，它是一个超立方体（或称双奇图，长度为的偶数循环）。特别是，所有凸循环都是 4 循环的部分立方图等价于近中值图。因此，我们得出结论：规则的近中值图恰好是超立方体，这推广了穆德的结果--规则的中值图是超立方体。

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 .