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

Akihiro Higashitani; Kazuki Kurimoto; Naoki Matsumoto

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

Discrete Mathematics 2020-02-26 v1 Combinatorics

Authors: Akihiro Higashitani , Kazuki Kurimoto , Naoki Matsumoto

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.

Cite

@article{arxiv.2002.10679,
  title  = {Feedback game on $3$-chromatic Eulerian triangulations of surfaces},
  author = {Akihiro Higashitani and Kazuki Kurimoto and Naoki Matsumoto},
  journal= {arXiv preprint arXiv:2002.10679},
  year   = {2020}
}

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11 pages, 7 figures

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

Abstract

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