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 $P_m\square P_n$. We completely determine all N-positions (the root vertices where the first player wins) and all P-positions (the root vertices where the first player loses). Moreover, we give a winning strategy for the winner.
From: Panupong Vichitkunakorn [view email]
[v1]
Wed, 16 Apr 2025 14:57:08 UTC (42 KB)
[v2]
Mon, 27 Jul 2026 14:14:19 UTC (41 KB)
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