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arXiv · 1707.00263

Colouring games based on autotopisms of Latin hyper-rectangles

Stephan Dominique Andres·Raúl M. Falcón
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Abstract

Every partial colouring of a Hamming graph is uniquely related to a partial Latin hyper-rectangle. In this paper we introduce the $\Theta$-stabilized $(a,b)$-colouring game for Hamming graphs, a variant of the $(a,b)$-colouring game so that each move must respect a given autotopism $\Theta$ of the resulting partial Latin hyper-rectangle. We examine the complexity of this variant by means of its chromatic number. We focus in particular on the bi-dimensional case, for which the game is played on the Cartesian product of two complete graphs, and also on the hypercube case.

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Stephan Dominique Andres, Raúl M. Falcón. 2017-07-02. Colouring games based on autotopisms of Latin hyper-rectangles. https://doi.org/10.2989/16073606.2018.1502214

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