发表机构
University of Bremen（不来梅大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究着色发现问题的参数化复杂性，针对三种修改模型给出固定参数算法与W[1]难下界，并证明四色情形在直径二图上仍NP完全。
AI 中文摘要
着色发现问题询问一个可能不恰当的初始着色是否能在规定数量的允许更改内变为恰当着色。我们研究了文献中先前研究过的三种修改步骤模型的参数化复杂性：重新着色一个顶点（颜色翻转）、交换任意顶点的颜色（颜色交换）以及仅跨边交换颜色（颜色滑动）。对于颜色翻转，我们给出了针对顶点覆盖和到完全图的距离这两个参数的精确固定参数算法。对于颜色交换，我们获得了针对顶点覆盖加上颜色数这一参数的固定参数可处理性。我们的下界表明，在颜色翻转模型中，针对树深度加上反馈顶点集是W[1]难的；在交换和滑动模型中，针对颜色数加上带宽或到不相交路径的距离是W[1]难的。所有三种变体在直径为二的图上使用四种颜色时仍然是NP完全的。
英文摘要
Coloring Discovery asks whether a possibly improper initial coloring can be made proper within a prescribed number of allowed changes. We study the parameterized complexity of three modification step models that were studied previously in the literature: recoloring one vertex (color flipping), swapping the colors of arbitrary vertices (color swapping), and swapping colors only across an edge (color sliding). For color flipping, we give exact fixed-parameter algorithms for the parameters vertex cover and distance to complete. For color swapping, we obtain fixed-parameter tractability for the parameter vertex cover plus the number of colors. Our lower bounds show W[1]-hardness for treedepth plus feedback vertex set in the color flipping model and for the number of colors plus bandwidth or distance to disjoint paths in the swapping and sliding models. All three variants remain NP-complete with four colors on graphs of diameter two.
Comments22 pages, 4 figures, submitted to SOFSEM 2027
