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On Tuza's conjecture for triangulations and graphs with small treewidth
Tuza (1981) conjectured that the size of a minimum set of edges
that intersects every triangle of a graph is at most twice the size
of a maximum set of edge-disjoint triangles of . In this paper we
present three results regarding Tuza's Conjecture. We verify it for graphs with
treewidth at most ; we show that for every
planar triangulation different from ; and that
if is a maximal graph with
treewidth 3. Our first result strengthens a result of Tuza, implying that
for every -free chordal graph