Rainbow Cliques in Edge-Colored Graphs

Let $G = (V,E)$ be an n-vertex graph and let c: E → N be a coloring of its edges. Let dᶜ(v) be the number of distinct colors on the edges at v ∈ V and let δᶜ(G) = minv ∈ V \ dᶜ(v) \. H. Li proved that δᶜ(G) > n/2 guarantees a rainbow triangle in G. We give extensions of Li's result to cliques Kᵣ for r ≥ 4.