Další formáty:
BibTeX
LaTeX
RIS
@article{1824821,
author = {Cooper, Jacob and Grzesik, Andrzej and Kabela, Adam and Kráľ, Daniel},
article_location = {LONDON},
article_number = {103462},
doi = {http://dx.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://dx.doi.org/10.1016/j.ejc.2021.103462.
|
