Packing Directed Cycles Quarter- and Half-Integrally

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Packing Directed Cycles Quarter- and Half-Integrally

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Packing Directed Cycles Quarter- and Half-Integrally

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Combinatorica

ISSN

0209-9683

e-ISSN

1439-6912

Svazek periodika

42

Číslo periodika v rámci svazku

supplement issue 2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

30

Strana od-do

1409-1438

Kód UT WoS článku

000857466700006

EID výsledku v databázi Scopus

2-s2.0-85130644399