On kernels for d-path vertex cover

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00379997" target="_blank" >RIV/68407700:21240/24:00379997 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jcss.2024.103531" target="_blank" >https://doi.org/10.1016/j.jcss.2024.103531</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcss.2024.103531" target="_blank" >10.1016/j.jcss.2024.103531</a>

Result language
angličtina
Original language name
On kernels for d-path vertex cover
Original language description
In this paper we study the kernelization of the d-Path Vertex Cover (d-PVC) problem. Given a graph G, the problem requires finding whether there exists a set of at most k vertices whose removal from G results in a graph that does not contain a path (not necessarily induced) with d vertices. It is known that d-PVC is NP-complete for d >= 2. Since the problem generalizes to d-Hitting Set, it is known to admit a kernel with O(dk(d)) edges. We improve on this by giving better kernels. Specifically, we give kernels with O(k(2)) vertices and edges for the cases when d = 4 and d = 5. Further, we give a kernel with O(k(4)d(2d+9)) vertices and edges for general d. (c) 2024 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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