Erdős problem 75
Is there a graph of chromatic number ℵ_ 1 with ℵ_ 1 vertices such that for all ε > 0, if n is sufficiently large and H is a subgraph on n vertices, then H contains an independent set of size > n ^ (1 - ε)?
Sources
FormalConjectures/ErdosProblems/
75.lean
Retained formal statement
Is there a graph of chromatic number ℵ_ 1 with ℵ_ 1 vertices such that for all ε > 0, if n is sufficiently large and H is a subgraph on n vertices, then H contains an independent set of size > n ^ (1 - ε)?
True ↔ ∃ V G, G.chromaticCardinal = Cardinal.aleph 1 ∧ Cardinal.mk V = Cardinal.aleph 1 ∧ ∀ ε > 0, ∀ᶠ (n : ℕ) in Filter.atTop, ∀ (H : G.Subgraph), H.verts.ncard = n → ∃ I, ↑I ⊆ H.verts ∧ G.IsIndepSet ↑I ∧ ↑I.card > ↑n ^ (1 - ε)OpenStatement only, no proof