Peg solitaire on graphs with jumping and merging allowed

Beeler, Robert A.; Kilby, Amanda

doi:10.2140/involve.2022.15.433

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2023

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“…In this model, the peg on x can jump over the peg on y and be placed on z if there exist two adjacent edges xy and yz. Solvability of peg solitaire on several graph classes has been studied ( [1], [2], [4], [6], [8]). Several variations of the game are also studied [5], [7], [9].…”

Section: Introductionmentioning

confidence: 99%

Solvability of Peg Solitaire on Graphs is NP-Complete

Ito

Takenaga

2023

IEICE Trans. Inf. & Syst.

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Peg solitaire is a single-player board game. The goal of the game is to remove all but one peg from the game board. Peg solitaire on graphs is a peg solitaire played on arbitrary graphs. A graph is called solvable if there exists some vertex s such that it is possible to remove all but one peg starting with s as the initial hole. In this paper, we prove that it is NP-complete to decide if a graph is solvable or not.

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