Falcón Ganfornina, Raúl ManuelAndres, Stephan Dominique2024-11-202024-11-202019Falcón Ganfornina, R.M. y Andres, S.D. (2019). Autotopism stabilized colouring games on rook's graphs. Discrete Applied Mathematics, 266, 200-212. https://doi.org/10.1016/j.dam.2019.05.006.1872-67710166-218Xhttps://hdl.handle.net/11441/164596This paper deals with the Θ-stabilized colouring game on the n × n rook’s graph, which constitutes a variant of the classical colouring game on finite graphs so that each configuration of the game is uniquely related to a partial Latin square of order n that respects a given autotopism Θ. The complexity of this variant is examined by means of its Θ-stabilized game chromatic number, whose currently known upper bound is improved to 2n−1. Particularly, we introduce the concept of a passing board that enables us to describe a constructive method to compute this number. Based on this method, we explicitly determine the game chromatic number associated to those n × n rook’s graphs, for which n ≤ 4.application/pdf13 p.engGraph colouring gamePartial Latin squareAutotopisminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.dam.2019.05.006