Erdős problem 1008

Does every graph with $m$ edges contain a subgraph with $\gg m^{2/3}$ edges which contains no $C_4$ ?

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

1008.lean

Retained formal statement2 of 4

Folkman's counterexample $K_{n,n^2}$ , which has $n^3$ edges, and yet every subgraph with $>n^2+\binom{n}{2}$ edges contains a $C_4$ .

FormalConjectures/ErdosProblems/1008.leanErdos1008.erdos_1008.variants.folkman4 linesExact file

1∀ (n : ℕ),2  (completeBipartiteGraph (Fin n) (Fin (n ^ 2))).edgeSet.ncard = n ^ 3 ∧3    ∀ H ≤ completeBipartiteGraph (Fin n) (Fin (n ^ 2)),4      n ^ 2 + n.choose 2 < H.edgeSet.ncard → (SimpleGraph.cycleGraph 4).IsContained H

SolvedStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures4
statement retained
VibeMathed0
not observed here
PLBY Lean proofs1
no statement retained
Jayyhk Erdős Lean1
no statement retained
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki1
no statement retained
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 1008.lean4