Feedback game on 3-chromatic Eulerian triangulations of surfaces

02/25/2020

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by   Akihiro Higashitani, et al.

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In this paper, we study the feedback game on 3-chromatic Eulerian triangulations of surfaces. We prove that the winner of the game on every 3-chromatic Eulerian triangulation of a surface all of whose vertices have degree 0 modulo 4 is always fixed. Moreover, we also study the case of 3-chromatic Eulerian triangulations of surfaces which have at least two vertices whose degrees are 2 modulo 4, and in particular, we determine the winner of the game on a concrete class of such graphs, called an octahedral path.