Connected Subtraction Games on Subdivided Stars

Antoine Dailly (1) , Julien Moncel (2) , Aline Parreau (1)

1 GOAL - Graphes, AlgOrithmes et AppLications
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes

The present paper deals with connected subtraction games in graphs, which are generalization of takeaway games. In a connected subtraction game, two players alternate removing a connected sub-graph from a given connected game-graph, provided the resulting graph is connected, and provided the number of vertices of the removed subgraph belongs to a prescribed set of integers. We derive general periodicity results on such games, as well as specific results when played on subdivided stars.

Mots clés: Combinatorial Games; Subtraction Games; Graphs

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Antoine Dailly, Julien Moncel, Aline Parreau. Connected Subtraction Games on Subdivided Stars. 2018. ⟨hal-01849181v1⟩