Erdős problem 1176
Let be a graph with chromatic number . Is it true that there is a colouring of the edges with many colours such that, in any countable colouring of the vertices, there exists a vertex colour containing all edge colours?
No current result
No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.
Retained declaration
FormalConjectures/ErdosProblems/1176.leanTrue ↔ ∀ {V : Type u_1} (G : SimpleGraph V), G.chromaticCardinal = Cardinal.aleph 1 → ∃ EColor, ∃ (_ : Cardinal.mk EColor = Cardinal.aleph 1), ∃ c_edge, ∀ (VColor : Type), Cardinal.mk VColor ≤ Cardinal.aleph 0 → ∀ (c_vert : V → VColor), ∃ vc, ∀ (ec : EColor), ∃ u v, ∃ (h : G.Adj u v), c_vert u = vc ∧ c_vert v = vc ∧ c_edge ⟨s(u, v), h⟩ = ecOpenStatement only, no proof