Undirected edge geography games on grids
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917986874425344 |
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| author | Sereekiatdilok, Tharit Vichitkunakorn, Panupong |
| author_facet | Sereekiatdilok, Tharit Vichitkunakorn, Panupong |
| contents | The undirected edge geography is a two-player combinatorial game on an undirected rooted graph. The players alternatively perform a move consisting of choosing an edge incident to the root vertex, removing the chosen edge, and marking the other endpoint as a new root vertex. The first player who cannot perform a move is the loser. In this paper, we are interested in the undirected edge geography game on the grid graph $P_m\square P_n$. We completely determine whether the root vertex is a winning position (N-position) or a losing position (P-position). Moreover, we give a winning strategy for the winner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Undirected edge geography games on grids Sereekiatdilok, Tharit Vichitkunakorn, Panupong Combinatorics 91A46, 05C57, 05C38 The undirected edge geography is a two-player combinatorial game on an undirected rooted graph. The players alternatively perform a move consisting of choosing an edge incident to the root vertex, removing the chosen edge, and marking the other endpoint as a new root vertex. The first player who cannot perform a move is the loser. In this paper, we are interested in the undirected edge geography game on the grid graph $P_m\square P_n$. We completely determine whether the root vertex is a winning position (N-position) or a losing position (P-position). Moreover, we give a winning strategy for the winner. |
| title | Undirected edge geography games on grids |
| topic | Combinatorics 91A46, 05C57, 05C38 |
| url | https://arxiv.org/abs/2504.12148 |