Title: Multicolor Turán numbers
Speaker: Letícia Mattos
Abstract: We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy, and Váli. Let G be the edge-disjoint union of k subgraphs F_i, where each F_i is isomorphic to a fixed graph F. We call a subgraph H of G multicolored if the edges of H belong to e(H) distinct F_i's. Define ex_F(H,n) to be the maximum value k such that there exists a graph G which is the edge-disjoint union of k graphs F_i on n vertices without a multicolored copy of H. We show that ex_{C_5}(C_3,n) is at most (1/25)n^2 + (3/25)n + o(n) and that all extremal graphs are close to a blow-up of the 5-cycle.
Joint work with Balogh, Liebenau and Morrison.
