On Tuza's Conjecture for Triangulations and Graphs with Small Treewidth
Fábio Botler, Cristina G. Fernandes, Juan Gutiérrez · Electronic Notes in Theoretical Computer Science · 2019
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 ) ≤ 3 2 ν ( G ) for every planar triangulation G different from K 4 ; and that τ ( G ) ≤ 9 5 ν ( G ) + 1 5 if G is a maximal graph with treewidth 3.