Octal Games on Graphs: The game 0.33 on subdivided stars and bistars - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Access content directly
Journal Articles Theoretical Computer Science Year : 2018

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

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.
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Dates and versions

hal-01418153 , version 1 (16-12-2016)
hal-01418153 , version 2 (04-04-2018)
hal-01418153 , version 3 (05-06-2018)

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Cite

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, 2018, 746, pp.19-35. ⟨10.1016/j.tcs.2018.06.018⟩. ⟨hal-01418153v3⟩
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