Corpus ID: 237605215

# Peg solitaire and Conway's soldiers on infinite graphs

```@article{Vito2021PegSA,
title={Peg solitaire and Conway's soldiers on infinite graphs},
author={Valentino Vito},
journal={ArXiv},
year={2021},
volume={abs/2109.11128}
}```
• V. Vito
• Published 23 September 2021
• Mathematics, Computer Science
• ArXiv
Peg solitaire is traditionally a one-player game played on a grid board filled with pegs. The goal of the game is to have a single peg remaining on the board by sequentially jumping a peg over an adjacent peg onto an empty square while eliminating the jumped peg. Conway’s soldiers is a related game played on Z with pegs initially located on the half-space y ≤ 0. The goal is to bring a peg as far as possible on the board using peg solitaire jumps. Conway showed that bringing a peg to the line y… Expand

#### References

SHOWING 1-10 OF 26 REFERENCES
Peg Solitaire on Cartesian Products of Graphs
• Computer Science, Mathematics
• Graphs Comb.
• 2021
It is proved that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs. Expand
Triangular Puzzle Peg
• Mathematical Solitaires & Games
• 2019
Algorithmic traversals of infinite graphs, arXiv preprint (2018), available at https://arxiv.org/abs/1810.09974
• 2018
Fool's solitaire on joins and Cartesian products of graphs
• Computer Science, Mathematics
• Discret. Math.
• 2015
Peg solitaire is a game generalized to connected graphs by Beeler and Hoilman. In the game pegs are placed on all but one vertex. If x y z form a 3-vertex path and x and y each has a peg but z doesExpand
Peg solitaire on trees with diameter four
• Mathematics, Computer Science
• Australas. J Comb.
• 2015
In a 2011 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 was to classify solvable trees. InExpand
Reversible peg solitaire on graphs
• Mathematics, Computer Science
• Discret. Math.
• 2015
It is shown that in this game all non-star graphs that contain a vertex of degree at least three are solvable, that cycles and paths on n vertices, where n is divisible by 2 or 3, aresolvable, and that all other graphs are not solvable. Expand
Pegging Numbers For Various Tree Graphs
This work defines the pegging number as the smallest number of pegs needed to reach all the vertices in a graph no matter what the distribution, and compute the optimal-pegging numbers of complete binary trees and complete infinitary trees. Expand
Beeler and D . Paul Hoilman , Peg solitaire on graphs , Discrete Math . 311 ( 2011 ) , no . 20 , 2198 – 2202 . [ 4 ] , Peg solitaire on the windmill and the double star graphs . , Australas
• 2012
Fool's solitaire on graphs
• Mathematics
• 2012
In recent work by Beeler and Hoilman, the game of peg solitaire is generalized to arbitrary boards. These boards are treated as graphs in the combinatorial sense. Normally, the goal of peg solitaireExpand
Peg solitaire on the windmill and the double star graphs
• Mathematics, Computer Science
• Australas. J Comb.
• 2012
This paper extends the study of the game of peg solitaire to arbitrary boards by considering the windmill and the double star, and gives simple necessary and sufficient conditions for the solvability of each graph. Expand