On the Parameterized Complexity of Coloring Discovery

2026-09-09

AI Summary

研究了通过三种颜色修改模型（颜色翻转、颜色交换、颜色滑动）在限定修改次数内将初始着色调整为正确着色的问题，并分析了参数化复杂度。

Abstract

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.

Problem

• Coloring Discovery
• parameterized complexity
• color flipping
• color swapping
• color sliding

Innovation

• color flipping
• fixed-parameter algorithms
• vertex cover
• color swapping
• W[1]-hardness