Packing and covering directed triangles asymptotically

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00125213" target="_blank" >RIV/00216224:14330/22:00125213 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0195669821001566" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0195669821001566</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ejc.2021.103462" target="_blank" >10.1016/j.ejc.2021.103462</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Packing and covering directed triangles asymptotically

Popis výsledku v původním jazyce

A well-known conjecture of Tuza asserts that if a graph has at most t pairwise edge-disjoint triangles, then it can be made triangle-free by removing at most 2t edges. If true, the factor 2 would be best possible. In the directed setting, also asked by Tuza, the analogous statement has recently been proven, however, the factor 2 is not optimal. In this paper, we show that if an n-vertex directed graph has at most t pairwise arc-disjoint directed triangles, then there exists a set of at most 1.8t + o(n(2)) arcs that meets all directed triangles. We complement our result by presenting two constructions of large directed graphs with t is an element of Omega(n(2)) whose smallest such set has 1.5t - o(n(2)) arcs. (C) 2021 Elsevier Ltd. All rights reserved.

Název v anglickém jazyce

Packing and covering directed triangles asymptotically

Popis výsledku anglicky

A well-known conjecture of Tuza asserts that if a graph has at most t pairwise edge-disjoint triangles, then it can be made triangle-free by removing at most 2t edges. If true, the factor 2 would be best possible. In the directed setting, also asked by Tuza, the analogous statement has recently been proven, however, the factor 2 is not optimal. In this paper, we show that if an n-vertex directed graph has at most t pairwise arc-disjoint directed triangles, then there exists a set of at most 1.8t + o(n(2)) arcs that meets all directed triangles. We complement our result by presenting two constructions of large directed graphs with t is an element of Omega(n(2)) whose smallest such set has 1.5t - o(n(2)) arcs. (C) 2021 Elsevier Ltd. All rights reserved.

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

—

Svazek periodika

101

Číslo periodika v rámci svazku

103462

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

1-9

Kód UT WoS článku

000721356900012

EID výsledku v databázi Scopus

2-s2.0-85119050224