A Deletion Game on Graphs: Le Pic Arête

This paper presents a deletion game on graphs, called “Le Pic Arête.” Two players alternately remove an edge of a given graph. A player gets one point each time he isolates a vertex (so that he gets at most two points by edge deletion). When no edge remains, the player with the maximum number of points is declared the winner. For instance, if we consider this game on a grid, we have a variant of the famous “Dots and Boxes” game. Our study consists of finding an approximation of the value of any game configuration, i.e., the difference between the numbers of points attainable by both players (when each player is supposed to play his best strategy).