Autoparatopism stabilized colouring games on rook's graphs

Abstract

We introduce the autoparatopism variant of the autotopism stabilized colouring game on the n×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∈{Id,(12)} and π∈{(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.