Document Type

Article

Language

eng

Publication Date

7-17-2017

Publisher

Mathematical Sciences Publishers

Source Publication

Involve

Source ISSN

1944-4176

Abstract

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 x and y, with y also adjacent to a hole on vertex z, and jumps the peg on x over the peg ony to z, removing the peg on y. 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 x and z (with a hole on y) and merges them to a single peg on y. 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.

Comments

Published version. Involve, Vol. 11, No. 1 (2018): 53-66. DOI. © 2018 Mathematical Sciences Publishers. Used with permission.

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