论文标题
某些三角形晶格的顶点标记得分
Vertex-edge marking score of certain triangular lattices
论文作者
论文摘要
顶点标记游戏在图表上的两个玩家（$ g =（v，e）$之间玩，一个玩家标记了顶点和另一个标记边缘。玩家希望分别最大程度地减少/最大化的标记边缘数量到一个未标记的顶点。 $ g $的顶点边缘着色号是完美播放的最高得分。 Brešar等人，[4]，对于有限平面图的顶点边缘着色编号，给出了$ 5 $的上限。尚不清楚界限是否紧密。在本文中，对于[4]中的问题，我们表明，飞机的无限常规三角形的顶点颜色数为4。我们还提供了两种一般技术，使我们能够计算平面许多相关三角形的顶点颜色数。
The vertex-edge marking game is played between two players on a graph, $G=(V,E)$, with one player marking vertices and the other marking edges. The players want to minimize/maximize, respectively, the number of marked edges incident to an unmarked vertex. The vertex-edge coloring number for $G$ is the maximum score achievable with perfect play. Brešar et al., [4], give an upper bound of $5$ for the vertex-edge coloring number for finite planar graphs. It is not known whether the bound is tight. In this paper, in response to questions in [4], we show that the vertex-edge coloring number for the infinite regular triangularization of the plane is 4. We also give two general techniques that allow us to calculate the vertex-edge coloring number in many related triangularizations of the plane.
