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. Copyright © 2021 Colgate University. All rights reserved.
|Journal||INTEGERS: Electronic Journal of Combinatorial Number Theory|
|Early online date||01 Feb 2021|
|Publication status||Published - 2021|