研究 1-11 的新工具--图形表示法

IF 0.6 4区 数学 Q3 MATHEMATICS
Mikhail Futorny, Sergey Kitaev, Artem Pyatkin
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引用次数: 0

摘要

k-11-representable 图的概念由 Jeff Remmel 于 2017 年提出,Cheon 等人于 2019 年对其进行了研究,并将其作为已被广泛研究的词可表示图概念的自然扩展,而词可表示图正是 0-11-representable 图。如果一个图 G 可以用一个词 w 来表示,而对于 G 中的任何边(或者说,非边)xy,由 x 和 y 形成的 w 的子序列中最多包含 k(或者说,至少 \(k+1\))对连续相等的字母,那么这个图就是 k-11-representable 图。Cheon 等人的一个显著结果是,任何图都是 2-11-representable 的,而是否每个图都是 1-11-representable 则不得而知。Cheon 等人的研究表明,1-11-可表示图的类别严格大于词可表示图的类别,他们还引入了一个有用的工具箱来研究 1-11-representable 图。在本文中,我们介绍了研究 1-11 表示图的新工具。我们将它们用于建立 Chvátal 图、Mycielski 图、分裂图以及顶点可划分为可比图和独立集的图的 1-11 表示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

New Tools to Study 1-11-Representation of Graphs

New Tools to Study 1-11-Representation of Graphs

The notion of a k-11-representable graph was introduced by Jeff Remmel in 2017 and studied by Cheon et al. in 2019 as a natural extension of the extensively studied notion of word-representable graphs, which are precisely 0-11-representable graphs. A graph G is k-11-representable if it can be represented by a word w such that for any edge (resp., non-edge) xy in G the subsequence of w formed by x and y contains at most k (resp., at least \(k+1\)) pairs of consecutive equal letters. A remarkable result of Cheon at al. is that any graph is 2-11-representable, while it is unknown whether every graph is 1-11-representable. Cheon et al. showed that the class of 1-11-representable graphs is strictly larger than that of word-representable graphs, and they introduced a useful toolbox to study 1-11-representable graphs. In this paper, we introduce new tools for studying 1-11-representation of graphs. We apply them for establishing 1-11-representation of Chvátal graph, Mycielski graph, split graphs, and graphs whose vertices can be partitioned into a comparability graph and an independent set.

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来源期刊
Graphs and Combinatorics
Graphs and Combinatorics 数学-数学
CiteScore
1.00
自引率
14.30%
发文量
160
审稿时长
6 months
期刊介绍: Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.
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