A new analysis technique for the Sprouts Game
Riccardo Focardi, Flaminia L. Luccio · ARCA (Università Ca' Foscari Venezia) · 2001
Sprouts is a two players game that was first introduced by M.S. Patterson and J.H. Conway in 1967. There are two players A and B that starting from a set of x0 vertices draw a plane graph by alternatively connecting any pair of two vertices with degree less than three with an edge, and by inserting a new vertex in the new edge. The move is possible if and only if the new connection maintains the planarity of the graph. The player that executes the last possible move is the winner. We study some new topological properties of the Sprouts Game and we show their effectiveness by giving a complete analysis of the case x0 = 7, for which no formal proof is, to the best of our knowledge, known.