Vol. 5, No. 4, 2012

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ISSN: 1944-4184 (e-only)
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Fool's solitaire on graphs

Robert A. Beeler and Tony K. Rodriguez

Vol. 5 (2012), No. 4, 473–480
Abstract

In recent work by Beeler and Hoilman, the game of peg solitaire is generalized to arbitrary boards. These boards are treated as graphs in the combinatorial sense. Normally, the goal of peg solitaire is to minimize the number of pegs remaining at the end of the game. In this paper, we consider the open problem of determining the maximum number of pegs that can remain at the end of the game, under the restriction that we must jump whenever possible. In this paper, we give bounds for this number. We also determine it exactly for several well-known families of graphs. Several open problems regarding this number are also given.

Keywords
peg solitaire, games on graphs, combinatorial games, graph theory
Mathematical Subject Classification 2010
Primary: 05C57
Secondary: 91A43
Milestones
Received: 23 January 2012
Revised: 20 April 2012
Accepted: 22 May 2012
Published: 14 June 2013

Communicated by Joseph Gallian
Authors
Robert A. Beeler
Department of Mathematics and Statistics
East Tennessee State University
Johnson City, TN 37614
United States
Tony K. Rodriguez
Department of Mathematics and Statistics
East Tennessee State University
Johnson City, TN 37614
United States