Octal Games on Graphs: The game 0.33 on subdivided stars and bistars

Laurent Beaudou 1 Pierre Coupechoux 2 Antoine Dailly 3 Sylvain Gravier 4 Julien Moncel 2 Aline Parreau 3 Eric Sopena 5
1 UCA - Université Clermont Auvergne
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
3 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
4 IF - Institut Fourier
5 LaBRI - Laboratoire Bordelais de Recherche en Informatique
Abstract : Octal games are a well-defined family of two-player games played on heaps of counters, in which the players remove alternately a certain number of counters from a heap, sometimes being allowed to split a heap into two nonempty heaps, until no counter can be removed anymore. We extend the definition of octal games to play them on graphs: heaps are replaced by connected components and counters by vertices. Thus, an octal game on a path P_n is equivalent to playing the same octal game on a heap of n counters. We study one of the simplest octal games, called 0.33, in which the players can remove one vertex or two adjacent vertices without disconnecting the graph. We study this game on trees and give a complete resolution of this game on subdivided stars and bistars.
Keywords : Combinatorial Games Subtraction Games Graphs Octal Games
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Submitted on : Tuesday, June 5, 2018 - 3:50:16 PM
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EC-LYON | FOURIER | INSMI | UNIV-BORDEAUX | TDS-MACS | LABRI | UGA | UNIV-LYON2 | UNIV-LYON1 | INSA-LYON | INSA-TOULOUSE | PRES_CLERMONT | LIRIS | LAAS-DECISION-ET-OPTIMISATION | LAAS | LAAS-ROC | ACL-SF | INSA-GROUPE | UNIV-TLSE3

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Laurent Beaudou, Pierre Coupechoux, Antoine Dailly, Sylvain Gravier, Julien Moncel, et al.. Octal Games on Graphs: The game 0.33 on subdivided stars and bistars. Theoretical Computer Science, Elsevier, 2018, 746, pp.19-35. ⟨10.1016/j.tcs.2018.06.018⟩. ⟨hal-01418153v3⟩

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