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Full-Text Articles in Physical Sciences and Mathematics
Peg Solitaire On Graphs In Which We Allow Merging And Jumping, Amanda L. Mckinney
Peg Solitaire On Graphs In Which We Allow Merging And Jumping, Amanda L. Mckinney
Undergraduate Honors Theses
Peg solitaire is a game in which pegs are placed in every hole but one and the player jumps over pegs along rows or columns to remove them. Usually, the goal of the player is to leave only one peg. In a 2011 paper, this game is generalized to graphs. In this thesis, we consider a variation of peg solitaire on graphs in which pegs can be removed either by jumping them or merging them together. To motivate this, we survey some of the previous papers in the literature. We then determine the solvability of several classes of graphs including …
Peg Solitaire On Trees With Diameter Four, Clayton A. Walvoort
Peg Solitaire On Trees With Diameter Four, Clayton A. Walvoort
Electronic Theses and Dissertations
In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.