The Erdos-Lovasz Cover Number Problem
Prior state unknown→proved
an improved lower bound; the true order of g(r) remains open
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
combinatorics / Extremal combinatorics
The Erdos-Lovasz Cover Number Problem
Let $g(r)$ be the fewest edges in an $r$-uniform intersecting hypergraph with cover number $r$. Erdos and Lovasz proved $g(r) \ge 8r/3 - 3$. An elementary argument gives $g(r) \ge 3r - 4$, and building on it with Kahn's small-codegree edge-colouring theorem pushes the bound further.
20Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts
Temporal state
Current frontier
No reconciled state yet.
Append-only history
Frontier timeline
Research memory
Claims and attempts
Scoped claims
Let $g(r)$ be the fewest edges in an $r$-uniform intersecting hypergraph with cover number $r$. Erdos and Lovasz proved $g(r) \ge 8r/3 - 3$. An elementary argument gives $g(r) \ge 3r - 4$, and building on it with Kahn's small-codegree edge-colouring theorem pushes the bound further.
an improved lower bound; the true order of g(r) remains open
Recorded attempts
Evidence graph
Connected research record
No public relationships recorded yet.