Erdős problem 794 · problems.science

Is it true that every $3$ -uniform hypergraph on $3n$ vertices with at least $n^3+1$ edges must contain either a subgraph on $4$ vertices with $3$ edges or a subgraph on $5$ vertices with $7$ edges?

Sources

Browse retained paths and inspect the exact material available for this Problem.

4 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

794.lean

Retained formal statement2 of 4

Balogh has observed that this problem is probably misstated by Erdős - indeed, every graph with $5$ vertices spanning $7$ edges contains a graph on $4$ vertices spanning $3$ edges, so the second condition can be dropped.

FormalConjectures/ErdosProblems/794.leanErdos794.erdos_794.variants.balogh2 linesExact file

1∀ {V : Type u_1} [inst : DecidableEq V] (H : Finset (Finset V)),2  H.IsThreeUniform → H.ContainsSubgraph 5 7 → H.ContainsSubgraph 4 3

SolvedStatement only, no proof

Sources

Search problems.science