Thresholds for the monochromatic clique transversal game

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-03-01 DOI:10.1016/j.exmath.2022.11.001

Csilla Bujtás , Pakanun Dokyeesun , Sandi Klavžar

引用次数: 1

Abstract

We study a recently introduced two-person combinatorial game, the $(a, b)$ -monochromatic clique transversal game which is played by Alice and Bob on a graph $G$ . As we observe, this game is equivalent to the $(b, a)$ -biased Maker–Breaker game played on the clique-hypergraph of $G$ . Our main results concern the threshold bias $a_{1} (G)$ that is the smallest integer $a$ such that Alice can win in the $(a, 1)$ -monochromatic clique transversal game on $G$ if she is the first to play. Among other results, we determine the possible values of $a_{1} (G)$ for the disjoint union of graphs, prove a formula for $a_{1} (G)$ if $G$ is triangle-free, and obtain the exact values of $a_{1} (C_{n} □ C_{m})$ , $a_{1} (C_{n} □ P_{m})$ , and $a_{1} (P_{n} □ P_{m})$ for all possible pairs $(n, m)$ .

查看原文本刊更多论文

单色集团横向博弈的阈值

最近介绍二人组合游戏,我们研究(a, b)单色集团横向游戏由爱丽丝和鲍勃在一个图G .我们观察,这个游戏相当于(b, a)偏见Maker-Breaker游戏的clique-hypergraph G .我们的主要结果担心阈值偏差a1 (G)是最小的整数,爱丽丝可以赢得(a, 1)单色集团横向游戏G如果她是第一次玩。在其他结果中，我们确定了图的不相交并的a1(G)的可能值，证明了如果G是无三角形的a1(G)的一个公式，并获得了所有可能对(n,m)的a1(Cn□Cm)， a1(Cn□Pm)和a1(Pn□Pm)的精确值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

期刊介绍： Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.