The graph distance game
Wayne Goddard, Anne Sinko, Peter J. Slater, Honghai Xu · 2011
In the graph distance game, two players alternate in constructing a max-imal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to min-imize. In this note, we examine the distance game for various graphs, and provide general bounds, exact results for special graphs, and an algorithm for trees. Computer calculations suggest interesting conjectures for grids. 1