Freely Solvable Graphs in Peg Solitaire. (2nd September 2013)

• Record Type: Journal Article
• Authors: Beeler, Robert A.; Gray, Aaron D.
• Other Names: Dondi R. Academic Editor.; Gordon N. A. Academic Editor.; Jou M.-j. Academic Editor.; Traldi L. Academic Editor.; Zagaglia N. Academic Editor.
• Is Part Of: ISRN combinatorics. Volume 2013(2013)
• Publication Date: 2013-09-02
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Electronic journals; Periodicals; 511.6
• DOI: 10.1155/2013/605279
• Languages: English
• ISSNs: 2090-8911

Abstract

Abstract : 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.