On Tuza's conjecture for triangulations and graphs... - BV FAPESP
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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On Tuza's conjecture for triangulations and graphs with small treewidth

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Author(s):
Botler, Fabio [1] ; Fernandes, Cristina G. [2] ; Gutierrez, Juan [3]
Total Authors: 3
Affiliation:
[1] Univ Fed Rio de Janeiro, Programa Engn Sistemas & Comp, COPPE, Rio De Janeiro - Brazil
[2] Univ Sao Paulo, Dept Ciencia Comp, Sao Paulo - Brazil
[3] Univ Ingn & Tecnol UTEC, Dept Ciencia Comp, Barranco - Peru
Total Affiliations: 3
Document type: Journal article
Source: DISCRETE MATHEMATICS; v. 344, n. 4 APR 2021.
Web of Science Citations: 0
Abstract

Tuza (1981) conjectured that the size tau(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the size nu(G) of a maximum set of edge disjoint triangles of G. In this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; we show that tau(G) <= 3/2 nu(G) for every planar triangulation G different from K-4; and that tau(G) <= 9/5 nu(G) + 1/5 if G is a maximal graph with treewidth 3. Our first result strengthens a result of Tuza, implying that tau(G) <= 2 nu(G) for every K-8-free chordal graph G. (C) 2020 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 15/08538-5 - Graph transversals
Grantee:Juan Gabriel Gutierrez Alva
Support Opportunities: Scholarships in Brazil - Doctorate