On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth

F. Botler; C. G. Fernandes; J. Gutiérrez

doi:10.1016/j.entcs.2019.08.016

On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth

F. Botler, C. G. Fernandes, J. Gutiérrez

Research output: Contribution to journal › Conference article › peer-review

5 Scopus citations

Abstract

Tuza (1981) conjectured that the cardinality τ(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the cardinality ν(G) of a maximum set of edge-disjoint triangles of G. I this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; and we show that _{^{τ(G)≤32ν(G)}} for every planar triangulation G different from K₄; and that _{^{τ(G)≤95ν(G)+15}} if G is a maximal graph with treewidth 3.

Original language	English
Pages (from-to)	171-183
Number of pages	13
Journal	Electronic Notes in Theoretical Computer Science
Volume	346
DOIs	https://doi.org/10.1016/j.entcs.2019.08.016
State	Published - 2019
Externally published	Yes
Event	10th Latin and American Algorithms, Graphs and Optimization Symposium, LAGOS 2019 - Belo Horizonte, Brazil Duration: 2 Jun 2019 → 7 Jun 2019

Keywords

Triangle transversal
treewidth
triangle packing
triangulation

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10.1016/j.entcs.2019.08.016

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@article{91c22f4e31c446df96fbd1165a7350ab,

title = "On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth",

abstract = "Tuza (1981) conjectured that the cardinality τ(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the cardinality ν(G) of a maximum set of edge-disjoint triangles of G. I this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; and we show that τ(G)≤32ν(G) for every planar triangulation G different from K4; and that τ(G)≤95ν(G)+15 if G is a maximal graph with treewidth 3.",

keywords = "Triangle transversal, treewidth, triangle packing, triangulation",

author = "F. Botler and Fernandes, {C. G.} and J. Guti{\'e}rrez",

note = "Publisher Copyright: {\textcopyright} 2019 The Author(s).; 10th Latin and American Algorithms, Graphs and Optimization Symposium, LAGOS 2019 ; Conference date: 02-06-2019 Through 07-06-2019",

year = "2019",

doi = "10.1016/j.entcs.2019.08.016",

language = "English",

volume = "346",

pages = "171--183",

journal = "Electronic Notes in Theoretical Computer Science",

issn = "1571-0661",

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TY - JOUR

T1 - On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth

AU - Botler, F.

AU - Fernandes, C. G.

AU - Gutiérrez, J.

PY - 2019

Y1 - 2019

N2 - Tuza (1981) conjectured that the cardinality τ(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the cardinality ν(G) of a maximum set of edge-disjoint triangles of G. I this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; and we show that τ(G)≤32ν(G) for every planar triangulation G different from K4; and that τ(G)≤95ν(G)+15 if G is a maximal graph with treewidth 3.

AB - Tuza (1981) conjectured that the cardinality τ(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the cardinality ν(G) of a maximum set of edge-disjoint triangles of G. I this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; and we show that τ(G)≤32ν(G) for every planar triangulation G different from K4; and that τ(G)≤95ν(G)+15 if G is a maximal graph with treewidth 3.

KW - Triangle transversal

KW - treewidth

KW - triangle packing

KW - triangulation

UR - http://www.scopus.com/inward/record.url?scp=85076255155&partnerID=8YFLogxK

U2 - 10.1016/j.entcs.2019.08.016

DO - 10.1016/j.entcs.2019.08.016

M3 - Conference article

AN - SCOPUS:85076255155

SN - 1571-0661

VL - 346

SP - 171

EP - 183

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

T2 - 10th Latin and American Algorithms, Graphs and Optimization Symposium, LAGOS 2019

Y2 - 2 June 2019 through 7 June 2019

ER -

On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth

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