In this paper, we study several coloring problems on graphs from the viewpoint of parameterized complexity. We show that Precoloring Extension is fixed-parameter tractable (FPT) parameterized by distance to clique and Equitable Coloring is FPT parameterized by the distance to threshold graphs. We also study the List k-Coloring and show that the problem is NP-complete on split graphs and it is FPT parameterized by solution size on split graphs.

中文翻译：

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阈值图上的参数化着色问题

在本文中，我们从参数化复杂度的角度研究了图上的几个着色问题。我们表明，预着色扩展是固定参数易处理 (FPT)，由到集团的距离参数化，而公平着色是由到阈值图的距离参数化的 FPT。我们还研究了 List k-Coloring 并表明问题在分割图上是 NP 完全的，并且它是由分割图上的解决方案大小参数化的 FPT。