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Rooks and Arc-Kayles

Ponente: Antoine Dailly
Institución: LIRIS, Universidad de Lyon
Tipo de Evento: Investigación
Cuándo 13/12/2017
de 17:00 a 18:00
Dónde Unidad Multidisciplinaria de Docencia e Investigación (UMDI), Aula 2. UNAM Campus Juriquilla, Querétaro
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The non-attacking queens game was introduced by Noon and Van Brummelen as a variation on the well-known queens problem. We study a variation, where the players alternate placing rooks on a holed chessboard such that they are not attacked by an already placed rook. Rooks cannot attack through holes. The first player unable to place a rook loses.
We represent this game as a game on weighted graphs. The players alternate choosing an edge, and decrease the weights of its end vertices by 1. A vertex with weight 0 cannot be played anymore. The first player unable to select an edge loses. We call this game Weighted Arc-Kayles (WAK for short).
During this talk, I will give an introduction to Sprague-Grundy theory, which is used to study this kind of games. I will then present our main result, which is the study of the case when there is one hole on the side of the chessboard. I will also show links between WAK and the well-known vertex deletion game Arc-Kayles.