Autoparatopism stabilized colouring games on rook's graphs

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.040

Stephan Dominique Andres, Helena Bergold, Raúl M. Falcón

引用次数: 4

Abstract

We introduce the autoparatopism variant of the autotopism stabilized colouring game on the $n \times n$ rook's graph as a natural generalization of the latter so that each board configuration is uniquely related to a partial Latin square of order n that respects a given autoparatopism (θ; π). To this end, we distinguish between $π \in {Id, (12)}$ and $π \in {(13), (23), (123), (132)}$ . The complexity of this variant is examined by means of the autoparatopism stabilized game chromatic number. Some illustrative examples and results are shown.

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自斜视在rook的图形上稳定了着色游戏

我们在n×n车图上引入自自论稳定着色游戏的自自自论变体，作为后者的自然推广，使得每个棋盘构型都与尊重给定自自自自性的n阶部分拉丁方唯一相关(θ;π)。为此,我们区分π∈{Id(12)}和π∈{(13)、(23)、(123)、(132)}。该变异的复杂性是通过自拟真稳定博弈色数来检验的。给出了一些说明性的例子和结果。

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

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

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