Frank Harary proposed the following game: Given a caterpillar C, two players take turns removing edges of a path. The player who takes the last edge wins the game. In this paper, we completely characterize the N-and P-positions for all caterpillars with spine length zero, one, two and three. Furthermore, we analyze approximately 94% of the caterpillars with spine length greater than or equal to four. In those cases, they all turn out to be N-positions.
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Mathematics and Statistics
Richard M. Low, Ardak Kapbasov, Arman Kapbasov, Stephen C. Locke, and W. H. Chan. "A codex of n-and p-positions in harary’s ‘caterpillar game’" Integers (2021): 1-26.