Merging Peg Solitaire in Graphs
Mathematical Sciences Publishers
Peg solitaire has recently been generalized to graphs. Here, pegs start on all but one of the vertices in a graph. A move takes pegs on adjacent vertices x and y, with y also adjacent to a hole on vertex z, and jumps the peg on x over the peg ony to z, removing the peg on y. The goal of the game is to reduce the number of pegs to one.
We introduce the game merging peg solitaire on graphs, where a move takes pegs on vertices x and z (with a hole on y) and merges them to a single peg on y. When can a configuration on a graph, consisting of pegs on all vertices but one, be reduced to a configuration with only a single peg? We give results for a number of graph classes, including stars, paths, cycles, complete bipartite graphs, and some caterpillars.