Table of Contents
ISRN Combinatorics
Volume 2013 (2013), Article ID 605279, 6 pages
Research Article

Freely Solvable Graphs in Peg Solitaire

Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614-1700, USA

Received 17 June 2013; Accepted 18 July 2013

Academic Editors: R. Dondi, N. A. Gordon, M.-j. Jou, L. Traldi, and N. Zagaglia

Copyright © 2013 Robert A. Beeler and Aaron D. Gray. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In a 2011 paper, the game of peg solitaire is generalized to arbitrary boards, which are treated as graphs in the combinatorial sense. Of particular interest are graphs that are freely solvable, that is, graphs that can be solved from any starting position. In this paper we give several examples of freely solvable graphs including all such trees with ten vertices or less, numerous cycles with a subdivided chord, meshes, and generalizations of the wheel, helm, and web.