论文标题
$（m，n）$ - 彩色混合图的颜色
Colourings of $(m, n)$-coloured mixed graphs
论文作者
论文摘要
在非正式上，混合图是从简单的无向图获得的对象，通过为其边缘的子集选择一个方向。混合图为$（m，n）$ - 如果分配了每个边缘的$ M \ geq 0 $颜色之一，并且将每个弧分配为$ n \ geq 0 $颜色之一。面向的图形为$（0，1）$ - 彩色混合图，2边色的图为$（2，0）$ - 彩色混合图。我们表明，Sopena用于定向图的顶点着色的结果，以及Kostochka，Sopena和Zhu的顶点颜色图和2边色的图形的结果，是有关$（M，N）$彩色混合图的顶点颜色的特殊情况。这两个都可以视为布鲁克斯定理的一种版本。
A mixed graph is, informally, an object obtained from a simple undirected graph by choosing an orientation for a subset of its edges. A mixed graph is $(m, n)$-coloured if each edge is assigned one of $m \geq 0$ colours, and each arc is assigned one of $n \geq 0$ colours. Oriented graphs are $(0, 1)$-coloured mixed graphs, and 2-edge-coloured graphs are $(2, 0)$-coloured mixed graphs. We show that results of Sopena for vertex colourings of oriented graphs, and of Kostochka, Sopena and Zhu for vertex colourings oriented graphs and 2-edge-coloured graphs, are special cases of results about vertex colourings of $(m, n)$-coloured mixed graphs. Both of these can be regarded as a version of Brooks' Theorem.
