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Peg solitaire on graphs with jumping and merging allowed

Robert A. Beeler and Amanda Kilby

Vol. 15 (2022), No. 3, 433–446

Peg solitaire is a one-player board game in which pegs are placed in every hole but one and the player jumps over pegs along rows or columns to remove them. Usually, the goal of the player is to leave only one peg. In a 2011 paper, this game was generalized to graphs. We consider a new variant of peg solitaire on graphs in which pegs can be removed either by jumping them or by merging them together. For this variant, we show that several classes of graphs are solvable. These graphs include stars, caterpillars, trees of diameter 4, trees of diameter 5, and articulated caterpillars. We conclude this paper with several open problems related to this study.

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games on graphs, peg solitaire, merging peg solitaire
Mathematical Subject Classification
Primary: 05C57
Secondary: 91A43, 91A46
Received: 6 May 2021
Revised: 4 October 2021
Accepted: 23 November 2021
Published: 2 December 2022

Communicated by Kenneth S. Berenhaut
Robert A. Beeler
Department of Mathematics and Statistics
East Tennessee State University
Johnson City, TN
United States
Amanda Kilby
Department of Mathematics and Statistics
East Tennessee State University
Johnson City, TN
United States