A modular approach to Sprouts (Q1765239)

This paper investigates a two players game so-called Sprouts. The are two players \(A\) and \(B\) that, starting from a set of \(x_0\) vertices, build a graph by alternatively connecting any two vertices with degree less than three an edge, and by drawing a new vertex on this new edge. A move is allowed only if the new connection maintains the planarity of the graph. The player that executes the last possible move is the winner. The authors studies some new topological properties of this game and they show their effectiveness by giving a complete analysis of the case \(x_0=7\) for which, to the best of our knowledge, no formal proof has been previously given.