Kernelization of Graph Hamiltonicity: Proper H-Graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10439055" target="_blank" >RIV/00216208:11320/21:10439055 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/21:00350652
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wQHkVTwu2J" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wQHkVTwu2J</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1299001" target="_blank" >10.1137/19M1299001</a>
Alternative languages
Result language
angličtina
Original language name
Kernelization of Graph Hamiltonicity: Proper H-Graphs
Original language description
We obtain new polynomial kernels and compression algorithms for Path Cover and Cycle Cover, the well-known generalizations of the classical Hamiltonian Path and Hamiltonian Cycle problems. Our choice of parameterization is strongly influenced by the work of Bir'o, Hujter, and Tuza, who in 1992 introduced H-graphs, intersection graphs of connected subgraphs of a subdivision of a fixed (multi-)graph H. In this work, we turn to proper H-graphs, where the containment relationship between the representations of the vertices is forbidden. As the treewidth of a graph measures how similar the graph is to a tree, the size of graph H is the parameter measuring the closeness of the graph to a proper interval graph. We prove the following results. Path Cover admits a kernel of size O (parallel to H parallel to(8)), where parallel to H parallel to is the size of graph H. In other words, we design an algorithm that for an n-vertex graph G and integer k geq 1, in time polynomial in n and parallel to H parallel to, outputs a graph Gprime of size scrO (parallel to H parallel to(8)) and kprime leq | V (G' such that the vertex set of G is coverable by k vertex-disjoint paths if and only if the vertex set of G' is coverable by k' vertex-disjoint paths. Hamiltonian Cycle admits a kernel of size O (parallel to H parallel to(8)). Cycle Cover admits a polynomial kernel. We prove it by providing a compression of size O (parallel to H parallel to(10)) into another NP-complete problem, namely, Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and parallel to H parallel to, outputs an equivalent instance of Prize Collecting Cycle Cover of sizeO (parallel to H parallel to(10)). In all our algorithms we assume that a proper H-decomposition is given as a part of the input.
Czech name
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Czech description
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Classification
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)
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
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Volume of the periodical
35
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
53
Pages from-to
840-892
UT code for WoS article
000674142200010
EID of the result in the Scopus database
2-s2.0-85105713363