In 2011, Beeler and Hoilman generalised the game of peg solitaire to arbitrary connected graphs. Since then, peg solitaire and related games have been considered on many graph classes. In this paper, we introduce a variant of the game peg solitaire, called path-stick solitaire, which is played with sticks in edges instead of pegs in vertices. We prove several analogues to peg solitaire results for that game, mainly regarding different graph classes. Furthermore, we characterise, with very few exceptions, path-stick-solvable joins of graphs and provide some possible future research questions.
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de Wiljes, Jan-Hendrik and Kreh, Martin
"Path-Stick Solitaire on Graphs,"
Theory and Applications of Graphs: Vol. 9:
2, Article 12.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss2/12