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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
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Abstract |
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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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Keywords
games on graphs, peg solitaire, merging peg solitaire
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Mathematical Subject Classification
Primary: 05C57
Secondary: 91A43, 91A46
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Milestones
Received: 6 May 2021
Revised: 4 October 2021
Accepted: 23 November 2021
Published: 2 December 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Robert A. Beeler | |
| Department of Mathematics and
Statistics East Tennessee State University Johnson City, TN United States |
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| Amanda Kilby | |
| Department of Mathematics and
Statistics East Tennessee State University Johnson City, TN United States |
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