将符号图的消色差数推广到Zaslavsky染色
Generalising the achromatic number to Zaslavsky's colourings of signed graphs
摘要：
图的色数是图的色理论中最核心的概念之一，它指的是使图的顶点正确着色所需的最少颜色数。它的几个方面的利益已在文献中进行了调查，包括适当的着色修改的变体。这些变体包括，值得注意的是，图的无色数，这是正确着色图的顶点所需的最大颜色数，以便沿着某条边分配不同颜色的每个可能组合。这个参数的行为导致了许多有趣的研究，揭示了与色数的相似性和差异。这项工作发生在最近的一个趋势，旨在扩展色理论的图的领域签署的图，特别是在调查经典的结果如何适应签署的上下文中。大部分的工作都在这条线上的日期是关于两个主要的概括适当着色的签署图，归因于Zaslavsky和Guenin。将无色数推广到签名图是最近由Lajou发起的，他的调查与Guenin的着色有关。我们在这里继续这条研究路线，但把扎斯拉夫斯基的着色作为我们的适当着色的概念。我们研究的一般行为，我们所得到的变种的无色数，主要是通过调查如何已知的经典无色数的结果概括到我们的上下文。我们的研究结果涵盖，特别是，边界，标准操作图，和复杂性方面。
英文摘要：
The chromatic number, which refers to the minimum number of colours required to colour the vertices of graphs properly, is one of the most central notions of the graph chromatic theory. Several of its aspects of interest have been investigated in the literature, including variants for modifications of proper colourings. These variants include, notably, the achromatic number of graphs, which is the maximum number of colours required to colour the vertices of graphs properly so that each possible combination of distinct colours is assigned along some edge. The behaviours of this parameter have led to many investigations of interest, bringing to light both similarities and discrepancies with the chromatic number. This work takes place in a recent trend aiming at extending the chromatic theory of graphs to the realm of signed graphs, and, in particular, at investigating how classic results adapt to the signed context. Most of the works done in that line to date are with respect to two main generalisations of proper colourings of signed graphs, attributed to Zaslavsky and Guenin. Generalising the achromatic number to signed graphs was initiated recently by Lajou, his investigations being related to Guenin's colourings. We here pursue this line of research, but with taking Zaslavsky's colourings as our notion of proper colourings. We study the general behaviour of our resulting variant of the achromatic number, mainly by investigating how known results on the classic achromatic number generalise to our context. Our results cover, notably, bounds, standard operations on graphs, and complexity aspects.
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