论文标题
分区着色问题的复杂性
The Complexity of the Partition Coloring Problem
论文作者
论文摘要
给定一个简单的无向图$ g =（v，e）$，以及在$ p $ parts中的顶点集$ v $的分区，\ textsc {分区着色问题}询问我们是否可以从分区的每个部分中选择一个顶点，以使$ p $ pug选定的pug the of p $ p $ the the $ p $ thecssect the $ p $ by t by $ k $ by。 PCP是经典\ textsc {顶点着色问题}的广义问题，并且在许多领域（例如调度和编码等）都有应用程序。 在本文中，我们显示了\ textsc {分区着色问题的复杂性状态}，其中三个参数：颜色数量，分区的零件数以及分区每个部分的最大大小。 此外，我们为此问题提供了一种新的精确算法。
Given a simple undirected graph $G=(V,E)$ and a partition of the vertex set $V$ into $p$ parts, the \textsc{Partition Coloring Problem} asks if we can select one vertex from each part of the partition such that the chromatic number of the subgraph induced on the $p$ selected vertices is bounded by $k$. PCP is a generalized problem of the classical \textsc{Vertex Coloring Problem} and has applications in many areas, such as scheduling and encoding etc. In this paper, we show the complexity status of the \textsc{Partition Coloring Problem} with three parameters: the number of colors, the number of parts of the partition, and the maximum size of each part of the partition. Furthermore, we give a new exact algorithm for this problem.
