论文标题
$ 3 $ chronic Eulerian三角形的反馈游戏
Feedback game on $3$-chromatic Eulerian triangulations of surfaces
论文作者
论文摘要
在本文中，我们研究了$ 3 $ chromatic Eulerian表面三角形的反馈游戏。我们证明，游戏的获胜者在每3美元的欧拉晶体三角剖分中，其顶点均具有$ 0 $ modulo $ 4 $的表面始终是固定的。此外，我们还研究了$ 3 $ - 染色的Eulerian eulerian三角形的案例，这些表面至少具有两个顶点，其学位为$ 2 $ modulo $ 4 $，尤其是，我们在此类图中的一类游戏中确定了游戏的赢家，称为八面体路径。
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.
