Brouwer's conjecture: the sum of the t largest Laplacian eigenvalues of any graph is at most e(G) + t(t+1)/2.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 4/5
A well-known Laplacian eigenvalue conjecture, open ~15 years with wide partial results.
Attackability 3/5
Finite witness with cheap oracle, but extensive prior verification left little search room; fell to proof, not search.
- finite witness
- 5/5
- oracle cost
- 4/5
- freshness
- 1/5
- seedability
- 3/5
Confirmed resolution
proof by Kothari and Tudose on .
Full proof via an equivalence with the Grone-Merris-Bai theorem; cited as confirmed by subsequent July 2026 literature.
Claims
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No active claims.
Confirmed
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