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Packing Directed Cycles Quarter- and Half-Integrally

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455184" target="_blank" >RIV/00216208:11320/22:10455184 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FSUnV1HfBz" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FSUnV1HfBz</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s00493-021-4743-y" target="_blank" >10.1007/s00493-021-4743-y</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Packing Directed Cycles Quarter- and Half-Integrally

  • Original language description

    The celebrated Erdos-Posa theorem states that every undirected graph that does not admit a family of k vertex-disjoint cycles contains a feedback vertex set (a set of vertices hitting all cycles in the graph) of size O(k logk). The analogous result for directed graphs has been proven by Reed, Robertson, Seymour, and Thomas, but their proof yields a nonelementary dependency of the size of the feedback vertex set on the size of vertexdisjoint cycle packing. We show that we can obtain a polynomial bound if we relax the disjointness condition. More precisely, we show that if in a directed graph G there is no family of k cycles such that every vertex of G is in at most two (resp. four) of the cycles, then there exists a feedback vertex set in G of size O(k^6) (resp. O(k^4)). We show also variants of the above statements for butterfly minor models of any strongly connected digraph that is a minor of a directed cylindrical grid and for quarter-integral packings of subgraphs of high directed treewidth.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • 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

  • Continuities

    S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Combinatorica

  • ISSN

    0209-9683

  • e-ISSN

    1439-6912

  • Volume of the periodical

    42

  • Issue of the periodical within the volume

    supplement issue 2

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    30

  • Pages from-to

    1409-1438

  • UT code for WoS article

    000857466700006

  • EID of the result in the Scopus database

    2-s2.0-85130644399