Tuza's Conjecture for Maximum Degree at Most Seven
Prior state unknown→proved
Settles a class, not the conjecture: Tuza's conjecture remains open in general.
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combinatorics / Extremal graph theory
Tuza's Conjecture for Maximum Degree at Most Seven
Tuza conjectured that every finite simple graph satisfies $\tau(G) \leq 2\nu(G)$, where $\nu$ counts pairwise edge-disjoint triangles and $\tau$ is the fewest edges whose deletion leaves the graph triangle-free. Puleo had proved it for maximum average degree below 7. Proved here for every graph of maximum degree at most seven, crossing the equality boundary of Puleo's sparsity theorem.
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Tuza conjectured that every finite simple graph satisfies $\tau(G) \leq 2\nu(G)$, where $\nu$ counts pairwise edge-disjoint triangles and $\tau$ is the fewest edges whose deletion leaves the graph triangle-free. Puleo had proved it for maximum average degree below 7. Proved here for every graph of maximum degree at most seven, crossing the equality boundary of Puleo's sparsity theorem.
Settles a class, not the conjecture: Tuza's conjecture remains open in general.
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