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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%2F68407700%3A21240%2F19%3A00334116" target="_blank" >RIV/68407700:21240/19:00334116 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11320/19:10404857

  • Result on the web

    <a href="http://dx.doi.org/10.1007/978-3-030-24766-9_22" target="_blank" >http://dx.doi.org/10.1007/978-3-030-24766-9_22</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-030-24766-9_22" target="_blank" >10.1007/978-3-030-24766-9_22</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 Biró, 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(formula presented), that is, we design an algorithm that for an n-vertex graph G and an integer k>= 1, in time polynomial in n and (formula presented), outputs a graph G' of size (formula presented) and k'<= | 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.Cycle Cover admits a compression of size (formula presented) into another problem, called Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and (formula presented), outputs an equivalent instance of Prize Collecting Cycle Cover of size (formula presented). In all our algorithms we assume that a proper H-decomposition is given as a part of the input.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GA17-20065S" target="_blank" >GA17-20065S: Tight Parameterized Results for Directed Connectivity Problems</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2019

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    16th International Symposium on Algorithms and Data Structures (WADS 2019)

  • ISBN

    978-3-030-24765-2

  • ISSN

    0302-9743

  • e-ISSN

  • Number of pages

    15

  • Pages from-to

    296-310

  • Publisher name

    Springer

  • Place of publication

    Cham

  • Event location

    Edmonton

  • Event date

    Aug 5, 2019

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article