Communication Dans Un Congrès Année : 2025

Polynomial-time algorithms for Path Cover on trees and graphs of bounded treewidth

Résumé

In the Path Cover problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call Path Partition, is extensively studied, surprisingly little is known about Path Cover. We start filling this gap by designing a linear-time algorithm for Path Cover on trees. Let t be the treewidth of a given graph. We then show that Path Cover can be solved in polynomial time on graphs of bounded treewidth, in XP time n t O(t) , using a dynamic programming scheme. Our algorithm gives an FPT 2 O(t log t) n algorithm for Path Partition as a corollary. These results also apply to the variants where the paths are required to be induced (i.e. chordless) and/or edge-disjoint.

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hal-04931788 , version 1 (06-02-2025)

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Florent Foucaud, Atrayee Majumder, Tobias Mömke, Aida Roshany-Tabrizi. Polynomial-time algorithms for Path Cover on trees and graphs of bounded treewidth. 10th International Conference on Algorithms and Discrete Applied Mathematics (CALDAM 2025), Feb 2025, Coimbatore, India. pp.147-159, ⟨10.1007/978-3-031-83438-7_13⟩. ⟨hal-04931788⟩
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