$b$-Coloring Parameterized by Pathwidth is XNLP-complete

September 16, 2022 · The Ethereal · 🏛 arXiv.org

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Authors Lars Jaffke, Paloma T. Lima, Roohani Sharma arXiv ID 2209.07772 Category cs.CC: Computational Complexity Cross-listed cs.DS Citations 0 Venue arXiv.org Last Checked 3 months ago
Abstract
We show that the $b$-Coloring problem is complete for the class XNLP when parameterized by the pathwidth of the input graph. Besides determining the precise parameterized complexity of this problem, this implies that b-Coloring parameterized by pathwidth is $W[t]$-hard for all $t$, and resolves the parameterized complexity of $b$-Coloring parameterized by treewidth.
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