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Abstract
A k-path vertex cover (k-PVC) of a graph G is a vertex subset I such that each path on k vertices in G contains at least one member of I. Imagine that a token is placed on each vertex of a k-PVC. Given two k-PVCs I, J of a graph G, thek-Path Vertex Cover Reconfiguration (k-PVCR)} under Token Sliding (TS) problem asks if there is a sequence of k-PVCs between I and J where each intermediate member is obtained from its predecessor by sliding a token from some vertex to one of its unoccupied neighbors. This problem is known to be PSPACE-complete even for planar graphs of maximum degree 3 and bounded treewidth and can be solved in polynomial time for paths and cycles. Its complexity for trees remains unknown. In this paper, as a first step toward answering this question, for k ≥ 4, we present a polynomial-time algorithm that solves k-PVCR under TS for caterpillars (i.e., trees formed by attaching leaves to a path).
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Recommended Citation
Hoang, Duc A.
(2023)
"TS-Reconfiguration of k-Path Vertex Covers in Caterpillars for k \geq 4,"
Theory and Applications of Graphs: Vol. 10:
Iss.
1, Article 8.
DOI: 10.20429/tag.2023.10108
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/8
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