Packing and covering directed triangles asymptotically

J 2022

Packing and covering directed triangles asymptotically

COOPER, Jacob; Andrzej GRZESIK; Adam KABELA a Daniel KRÁĽ

Základní údaje

Originální název

Packing and covering directed triangles asymptotically

Autoři

COOPER, Jacob (826 Velká Británie a Severní Irsko, domácí); Andrzej GRZESIK; Adam KABELA (203 Česká republika, domácí) a Daniel KRÁĽ (203 Česká republika, garant, domácí)

Vydání

European Journal of Combinatorics, LONDON, ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2022, 0195-6698

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.000

Kód RIV

RIV/00216224:14330/22:00125213

Organizační jednotka

Fakulta informatiky

DOI

https://doi.org/10.1016/j.ejc.2021.103462

UT WoS

000721356900012

EID Scopus

2-s2.0-85119050224

Klíčová slova anglicky

directed graphs

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 13. 1. 2023 09:43, prof. RNDr. Daniel Kráľ, Ph.D., DSc.

Anotace

V originále

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.

Návaznosti

MUNI/A/1108/2020, interní kód MU

Název: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace X. (Akronym: SV-FI MAV X.)

Investor: Masarykova univerzita, Rozsáhlé výpočetní systémy: modely, aplikace a verifikace X.

MUNI/A/1145/2021, interní kód MU

Název: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace XI. (Akronym: SV-FI MAV XI.)

Investor: Masarykova univerzita, Rozsáhlé výpočetní systémy: modely, aplikace a verifikace XI.

MUNI/I/1677/2018, interní kód MU

Název: MUNI AWARD in Science and Humanitites 1 (Akronym: MASH 1)

Investor: Masarykova univerzita, MUNI AWARD in Science and Humanitites 1, MASH - MUNI Award in Science and Humanities

Citovat

COOPER, Jacob; Andrzej GRZESIK; Adam KABELA a Daniel KRÁĽ. Packing and covering directed triangles asymptotically. European Journal of Combinatorics. LONDON: ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2022, roč. 101, č. 103462, s. 1-9. ISSN 0195-6698. Dostupné z: https://doi.org/10.1016/j.ejc.2021.103462.

@article{1824821,
   author = {Cooper, Jacob and Grzesik, Andrzej and Kabela, Adam and Kráľ, Daniel},
   article_location = {LONDON},
   article_number = {103462},
   doi = {https://doi.org/10.1016/j.ejc.2021.103462},
   keywords = {directed graphs},
   language = {eng},
   issn = {0195-6698},
   journal = {European Journal of Combinatorics},
   title = {Packing and covering directed triangles asymptotically},
   url = {https://www.sciencedirect.com/science/article/pii/S0195669821001566},
   volume = {101},
   year = {2022}
}

TY  - JOUR
ID  - 1824821
AU  - Cooper, Jacob - Grzesik, Andrzej - Kabela, Adam - Kráľ, Daniel
PY  - 2022
TI  - Packing and covering directed triangles asymptotically
JF  - European Journal of Combinatorics
VL  - 101
IS  - 103462
SP  - 1-9
EP  - 1-9
PB  - ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
SN  - 01956698
KW  - directed graphs
UR  - https://www.sciencedirect.com/science/article/pii/S0195669821001566
N2  - 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.
ER  -

COOPER, Jacob; Andrzej GRZESIK; Adam KABELA a Daniel KRÁĽ. Packing and covering directed triangles asymptotically. \textit{European Journal of Combinatorics}. LONDON: ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2022, roč.~101, č.~103462, s.~1-9. ISSN~0195-6698. Dostupné z: https://doi.org/10.1016/j.ejc.2021.103462.

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