Packing directed circuits quarter-integrally

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404211" target="_blank" >RIV/00216208:11320/19:10404211 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.ESA.2019.72" target="_blank" >https://doi.org/10.4230/LIPIcs.ESA.2019.72</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ESA.2019.72" target="_blank" >10.4230/LIPIcs.ESA.2019.72</a>

Result language
angličtina
Original language name
Packing directed circuits quarter-integrally
Original language description
The celebrated Erdös-Pósa 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 log k). After being known for long as Younger's conjecture, a similar statement for directed graphs has been proven in 1996 by Reed, Robertson, Seymour, and Thomas. However, in their proof, the dependency of the size of the feedback vertex set on the size of vertex-disjoint cycle packing is not elementary. We show that if we compare the size of a minimum feedback vertex set in a directed graph with quarter-integral cycle packing number, we obtain a polynomial bound. 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 four of the cycles, then there exists a feedback vertex set in G of size O(k^4). On the way there we prove a more general result about quarter-integral packing of subgraphs of high directed treewidth: for every pair of positive integers a and b, if a directed graph G has directed treewidth Omega(a^6 b^8 log^2(ab)), then one can find in G a family of a subgraphs, each of directed treewidth at least b, such that every vertex of G is in at most four subgraphs.
Czech name
—
Czech description
—

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
27th Annual European Symposium on Algorithms (ESA 2019)
ISBN
978-3-95977-124-5
ISSN
1868-8969
e-ISSN
—
Number of pages
13
Pages from-to
1-13
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Mnichov
Event date
Sep 9, 2019
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—

Similar results(10)