On Tuza's conjecture for triangulations and graphs with small treewidth
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Tuza (1981) conjectured that the size τ(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the size ν(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 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.
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