Connect Four and Graph Decomposition

Laurent Evain (1) , Mathias Lederer , Bjarke Hammersholt Roune

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

We introduce the standard decomposition, a way of decomposing a labeled graph into a sum of certain labeled subgraphs. We motivate this graph-theoretic concept by relating it to Connect Four decompositions of standard sets. We prove that all standard decompositions can be generated in polynomial time, which implies that all Connect Four decompositions can be generated in polynomial time.

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]; Combinatoire [math.CO]

Laurent Evain, Mathias Lederer, Bjarke Hammersholt Roune. Connect Four and Graph Decomposition. 2013. ⟨hal-00814130⟩