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Feedback game on $3$-chromatic Eulerian triangulations of surfaces

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arxiv 2002.10679 v1 pith:T33M4JPG submitted 2020-02-25 cs.DM math.CO

Akihiro Higashitani , Kazuki Kurimoto , Naoki Matsumoto This is my paper · ORCID
classification cs.DMmath.CO
keywords chromaticeuleriangamesurfacestriangulationsfeedbackmodulovertices
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abstract

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.

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