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Colouring games based on autotopisms of Latin hyper-rectangles. (arXiv:1707.00263v1 [math.CO])
来源于:arXiv
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. 查看全文>>