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Merging peg
solitaire on graphs
John Engbers and Ryan Weber
Vol. 11 (2018), No. 1, 53–66
DOI: 10.2140/involve.2018.11.53
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Abstract |
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Peg solitaire has recently been generalized to graphs. Here, pegs start on all but one of the vertices in a graph. A move takes pegs on adjacent vertices and , with also adjacent to a hole on vertex , and jumps the peg on over the peg on to , removing the peg on . The goal of the game is to reduce the number of pegs to one. We introduce the game merging peg solitaire on graphs, where a move takes pegs on vertices and (with a hole on ) and merges them to a single peg on . When can a configuration on a graph, consisting of pegs on all vertices but one, be reduced to a configuration with only a single peg? We give results for a number of graph classes, including stars, paths, cycles, complete bipartite graphs, and some caterpillars. |
Keywords
peg solitaire, games on graphs, graph theory
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Mathematical Subject Classification 2010
Primary: 05C57
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Milestones
Received: 14 February 2016
Revised: 5 August 2016
Accepted: 7 August 2016
Published: 17 July 2017
Communicated by Anant Godbole
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Authors |
| John Engbers | |
| Department of Mathematics,
Statistics and Computer Science Marquette University Milwaukee, WI 53201 United States |
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| Ryan Weber | |
| Department of Mathematics,
Statistics and Computer Science Marquette University Milwaukee, WI 53201 United States |
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