For every nontrivial connected graph, the minimum maximal matching number is at most the harmonic index (TxGraffiti conjecture, 2023).
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 1/5
Machine-generated 2023 conjecture known within automated conjecturing.
Attackability 5/5
Nine-vertex counterexample existed the whole time; the archetype of a ripe target.
- finite witness
- 5/5
- oracle cost
- 5/5
- freshness
- 3/5
- seedability
- 4/5
Confirmed resolution
counterexample by Bıyıkoğlu; smallest cases identified by Gupta on .
Refuted with unbounded violation ratio; the smallest counterexample is the friendship graph F4 on nine vertices, and the smallest tree counterexample is the subdivided star on eleven vertices.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
Confirmed
This entry no longer accepts claims or resolution reports.