Vol. 13, No. 5, 2020

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Peg solitaire in three colors on graphs

Tara C. Davis, Alexxis De Lamere, Gustavo Sopena, Roberto C. Soto, Sonali Vyas and Melissa Wong

Vol. 13 (2020), No. 5, 791–802
Abstract

Peg solitaire is a classical one-person game that has been played in various countries on different types of boards. Numerous studies have focused on the solvability of the games on these traditional boards and more recently on mathematical graphs. In this paper, we go beyond traditional peg solitaire and explore the solvability on graphs with pegs of more than one color and arrive at results that differ from previous works on the subject. This paper focuses on classifying the solvability of peg solitaire in three colors on several different types of common mathematical graphs, including the path, complete bipartite, and star. We also consider the solvability of peg solitaire on the Cartesian products of graphs.

Keywords
peg solitaire, combinatorial games, games on graphs
Mathematical Subject Classification 2010
Primary: 05C57
Secondary: 91A43
Milestones
Received: 13 September 2019
Revised: 26 March 2020
Accepted: 6 August 2020
Published: 5 December 2020

Communicated by Joseph A. Gallian
Authors
Tara C. Davis
Department of Mathematics
Hawaii Pacific University
Honolulu, HI
United States
Alexxis De Lamere
Department of Mathematics
Hawaii Pacific University
Honolulu, HI
United States
Gustavo Sopena
Department of Mathematics
California State University
Fullerton, CA
United States
Roberto C. Soto
Department of Mathematics
California State University
Fullerton, CA
United States
Sonali Vyas
Department of Mathematics
California State University
Fullerton, CA
United States
Melissa Wong
Department of Mathematics
California State University
Fullerton, CA
United States