A generalization of Arc-Kayles

Antoine Dailly (), Valentin Gledel and Marc Heinrich
Additional contact information
Antoine Dailly: Univ Lyon, Université Lyon 1, LIRIS UMR CNRS 5205
Valentin Gledel: Univ Lyon, Université Lyon 1, LIRIS UMR CNRS 5205
Marc Heinrich: Univ Lyon, Université Lyon 1, LIRIS UMR CNRS 5205

International Journal of Game Theory, 2019, vol. 48, issue 2, No 8, 511 pages

Abstract: Abstract 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.

Keywords: Combinatorial games; Arc-Kayles; Graphs (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00182-018-0639-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:48:y:2019:i:2:d:10.1007_s00182-018-0639-5

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-018-0639-5

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().