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
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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
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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