Path-Stick Solitaire on Graphs
نویسندگان
چکیده
In 2011, Beeler and Hoilman generalised the game of peg solitaire to arbitrary connected graphs. Since then, related games have been considered on many graph classes. this paper, we introduce a variant solitaire, called path-stick which is played with sticks in edges instead pegs vertices. We prove several analogues results for that game, mainly regarding different Furthermore, characterise, very few exceptions, path-stick-solvable joins graphs provide some possible future research questions.
منابع مشابه
Reversible peg solitaire on graphs
The game of peg solitaire on graphs was introduced by Beeler and Hoilman in 2011. In this game, pegs are initially placed on all but one vertex of a graph GG. If xyz forms a path in GG and there are pegs on vertices x and y but not z, then a jump places a peg on z and removes the pegs from x and y. A graph is called solvable if, for some configuration of pegs occupying all but one vertex, some ...
متن کاملSolitaire Clobber Played on Hamming Graphs
The one-player game Solitaire Clobber was introduced by Demaine et al. Beaudou et al. considered a variation called SC2. Black and white stones are located on the vertices of a given graph. A move consists in picking a stone to replace an adjacent stone of the opposite color. The objective is to minimize the number of remaining stones. The game is interesting if there is at least one stone of e...
متن کاملA solitaire game played on 2-colored graphs
We introduce a solitaire game played on a graph. Initially one disk is placed at each vertex, one face green and the other red, oriented with either color facing up. Each move of the game consists of selecting a vertex whose disk shows green, flipping over the disks at neighboring vertices, and deleting the selected vertex. The game is won if all vertices are eliminated. We derive a simple pari...
متن کاملPeg solitaire on the windmill and the double star graphs
In a 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. In this paper, we extend this study by considering the windmill and the double star. Simple necessary and sufficient conditions are given for the solvability of each graph. We also discuss an open problem concerning the range of val...
متن کاملFool's solitaire on joins and Cartesian products of graphs
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 xyz form a 3-vertex path and x and y each have a peg but z does not, then we can remove the pegs at x and y and place a peg at z. By analogy with the moves in the original game, this is called a jump. The goal of the peg solitaire game on graphs is to find jumps t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theory and applications of graphs
سال: 2022
ISSN: ['2470-9859']
DOI: https://doi.org/10.20429/tag.2022.090212