We generalize Davies’s famous example to a property of graphs: a graph (V, X) (V, X) is Davies if for every F: X → R F: X R, there is a collection g v: v ∈ V \gᵥ: v V\ of ω → R R functions such that F (v, w) = ∑ n > ω g v (n) g w (n) F (v, w) = ₍> gᵥ (n) gw (n) for v, w ∈ X \v, w\ X. We show that if C o l (X) ≤ ω 1 Col (X) ₁ and | X |
Péter Komjáth (Mon,) studied this question.