A new deletion game on graphs : Le Pic'arête

Lois Blanc (1) , Eric Duchene (1, 2) , Sylvain Gravier (3)

1 Leibniz - IMAG - Laboratoire Leibniz
2 LIESP - Laboratoire d'Informatique pour l'Entreprise et les Systèmes de Production
3 IF - Institut Fourier

This paper presents a eletion game on graph, called the "Pic'arete". Two players alternately remove an edge of a given graph, one player getting one point each time the deletion of an edge isolates a vertex (so that you can get at most 2 points by edge deleted). When no edge remains, the player who has the maximum number of points is declared the winner. For instance, if we consider this game on the grid graph, we obtain a variant of the famous Dots and Boxes game. Our study consists in trying to make an estimate of the value of an initial game configuration, i.e., the difference between the maxima numbers of points attainable by both players. Finding a winning strategy will lead us to define a classification of game configurations, according to the parity of their number of edges, vertices, and sizes of hanging trees.

Mots clés: Combinatorial games; graph theory

Domaines: Mathématique discrète [cs.DM]

Lois Blanc, Eric Duchene, Sylvain Gravier. A new deletion game on graphs : Le Pic'arête. Integers : Electronic Journal of Combinatorial Number Theory, 2006, 6, pp.#G2. ⟨hal-00407964⟩