Freely solvable graphs in peg solitaire (Q2449266)

Summary: In [\textit{R. A. Beeler} and \textit{D. P. Hoilman}, Discrete Math. 311, No. 20, 2198--2202 (2011; Zbl 1230.05211)], 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.