Packing and covering directed triangles asymptotically
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Packing and covering directed triangles asymptotically
Original language description
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.
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
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
European Journal of Combinatorics
ISSN
0195-6698
e-ISSN
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Volume of the periodical
101
Issue of the periodical within the volume
103462
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
9
Pages from-to
1-9
UT code for WoS article
000721356900012
EID of the result in the Scopus database
2-s2.0-85119050224