Compound Node-Kayles on Paths

Adrien Guignard (1) , Eric Sopena (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

In his celebrated book "On Number and Games" (Academic Press, New-York, 1976), J.H. Conway introduced twelve versions of compound games. We analyze these twelve versions for the Node-Kayles game on paths. For usual disjunctive compound, Node-Kayles has been solved for a long time under normal play, while it is still unsolved under misère play. We thus focus on the ten remaining versions, leaving only one of them unsolved.

Mots clés: Combinatorial game; Compound game; Graph game; Node-Kayles; Octal game 0.137

Domaines: Mathématique discrète [cs.DM]

Adrien Guignard, Eric Sopena. Compound Node-Kayles on Paths. Theoretical Computer Science, 2009, 410 (21-23), pp.2033-2044. ⟨10.1016/j.tcs.2008.12.053⟩. ⟨hal-00288659v2⟩