
On Reconfigurability of Target Sets
We study the problem of deciding reconfigurability of target sets of a g...
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Distributed Vertex Cover Reconfiguration
Reconfiguration schedules, i.e., sequences that gradually transform one ...
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Propagation via Kernelization: The Vertex Cover Constraint
The technique of kernelization consists in extracting, from an instance ...
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On Graphs with Minimal Eternal Vertex Cover Number
The eternal vertex cover problem is a variant of the classical vertex co...
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Path matrix and path energy of graphs
Given a graph G, we associate a path matrix P whose (i, j) entry represe...
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Bounds on SweepCovers by Functional Compositions of Ordered Integer Partitions and Raney Numbers
A sweepcover is a vertex separator in trees that covers all the nodes b...
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Asymptotic enumeration of digraphs and bipartite graphs by degree sequence
We provide asymptotic formulae for the numbers of bipartite graphs with ...
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Reconfiguring kpath vertex covers
A vertex subset I of a graph G is called a kpath vertex cover if every path on k vertices in G contains at least one vertex from I. The kPath Vertex Cover Reconfiguration (kPVCR) problem asks if one can transform one kpath vertex cover into another via a sequence of kpath vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of kPVCR from the viewpoint of graph classes under the wellknown reconfiguration rules: TS, TJ, and TAR. The problem for k=2, known as the Vertex Cover Reconfiguration (VCR) problem, has been wellstudied in the literature. We show that certain known hardness results for VCR on different graph classes including planar graphs, bounded bandwidth graphs, chordal graphs, and bipartite graphs, can be extended for kPVCR. In particular, we prove a complexity dichotomy for kPVCR on general graphs: on those whose maximum degree is 3 (and even planar), the problem is PSPACEcomplete, while on those whose maximum degree is 2 (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomialtime algorithms for kPVCR on trees under each of TJ and TAR. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given kpath vertex covers in a yesinstance. In particular, on paths, our constructed reconfiguration sequence is shortest.
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