On n-stars in colorings and orientations of graphs - Protasov, I.V. (Algebra and Discrete Mathematics, 2016)
An n-star S in a graph G is the union of geodesic intervals I1,…,Ik with common end O such that the subgraphs I1∖O,…,Ik∖O are pairwise disjoint and l(I1)+…+l(Ik)=n. If the edges of G are oriented, S is directed if each ray Ii is directed. For natural number n,r, we construct a graph G of diam(G)=n such that, for any r-coloring and orientation of E(G), there exists a directed n-star with monochrome rays of pairwise distinct colors.