Undirected edge geography games on grids
Combinatorics
2025-04-17 v1
Abstract
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 . 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.
Keywords
Cite
@article{arxiv.2504.12148,
title = {Undirected edge geography games on grids},
author = {Tharit Sereekiatdilok and Panupong Vichitkunakorn},
journal= {arXiv preprint arXiv:2504.12148},
year = {2025}
}