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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.08247 |
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| _version_ | 1866929589257764864 |
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| author | Fiorini, Eugene Fogler, Maxwell Levandosky, Katherine Lu, Bryan Porter, Jacob Woldar, Andrew |
| author_facet | Fiorini, Eugene Fogler, Maxwell Levandosky, Katherine Lu, Bryan Porter, Jacob Woldar, Andrew |
| contents | In this paper we study a variant of the solitaire game Lights-Out, where the player's goal is to turn off a grid of lights. This variant is a two-player impartial game where the goal is to make the final valid move. This version is playable on any simple graph where each node is given an assignment of either a 0 (representing a light that is off) or 1 (representing a light that is on). We focus on finding the Nimbers of this game on grid graphs and generalized Petersen graphs. We utilize a recursive algorithm to compute the Nimbers for 2 x n grid graphs and for some generalized Petersen graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Nature and Complexity of an Impartial Two-Player Variant of the Game Lights-Out Fiorini, Eugene Fogler, Maxwell Levandosky, Katherine Lu, Bryan Porter, Jacob Woldar, Andrew Combinatorics Computational Complexity In this paper we study a variant of the solitaire game Lights-Out, where the player's goal is to turn off a grid of lights. This variant is a two-player impartial game where the goal is to make the final valid move. This version is playable on any simple graph where each node is given an assignment of either a 0 (representing a light that is off) or 1 (representing a light that is on). We focus on finding the Nimbers of this game on grid graphs and generalized Petersen graphs. We utilize a recursive algorithm to compute the Nimbers for 2 x n grid graphs and for some generalized Petersen graphs. |
| title | On the Nature and Complexity of an Impartial Two-Player Variant of the Game Lights-Out |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2411.08247 |