Erdős problem 1036 · problems.science

Let $G$ be a graph on $n$ vertices which does not contain a trivial (empty or complete) graph on more than $c\log n$ vertices. Must $G$ contain at least $2^{\Omega_c(n)}$ many induced subgraphs which are not pairwise isomorphic?

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FormalConjectures/ErdosProblems/

1036.lean

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Erdős and Hajnal [ErHa89b] proved that if $G$ does not contain a complete bipartite graph or its complement on more than $c\log n$ vertices then $G$ contains at least $2^{\Omega_c(n)}$ many non-isomorphic induced subgraphs.

FormalConjectures/ErdosProblems/1036.leanErdos1036.erdos_1036.variants.erdos_hajnal8 linesExact file

1∀ (c : ℝ),2  0 < c →3    ∃ δ,4      0 < δ ∧5        ∀ᶠ (n : ℕ) in Filter.atTop,6          ∀ (G : SimpleGraph (Fin n)),7            Erdos1036.NoLargeInducedBipartite G (c * Real.log ↑n) →8              Erdos1036.HasManyNonIsomorphicInducedSubgraphs G (2 ^ (δ * ↑n))

SolvedStatement only, no proof

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