Colouring games based on autotopisms of Latin hyper-rectangles

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.

23 pages, 7 figures

References in corpus (2)

• The set of autotopisms of partial Latin squares
• Autoparatopisms of Quasigroups and Latin Squares

Cited by in corpus (1)

• Computing autotopism groups of partial Latin rectangles: a pilot study