A generalization of Arc-Kayles - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

A generalization of Arc-Kayles

Antoine Dailly
Valentin Gledel
Marc Heinrich

Résumé

The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with counters on the vertices. The two players alternate choosing an edge and removing one counter on both endpoints. An edge can no longer be selected if any of its endpoints has no counter left. The last player to play a move wins. We give a winning strategy for WAK on trees of depth 2. Moreover, we show that the Grundy values of WAK and Arc-Kayles are unbounded. We also prove a periodicity result on the outcome of WAK when the number of counters is fixed for all the vertices but one. Finally, we show links between this game and a variation of the non-attacking queens game on a chessboard.
Fichier principal
Vignette du fichier
articleRevised (1).pdf (527.41 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-01587921 , version 1 (14-09-2017)
hal-01587921 , version 2 (16-04-2018)
hal-01587921 , version 3 (04-10-2018)

Identifiants

Citer

Antoine Dailly, Valentin Gledel, Marc Heinrich. A generalization of Arc-Kayles. 2017. ⟨hal-01587921v2⟩
413 Consultations
232 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More