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

Author(s)

Botler, Fabio ^[1] ; Fernandes, Cristina G. ^[2] ; Gutierrez, Juan ^[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

• 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