Turán Density of 2-Edge-Colored Bipartite Graphs with Application on {2, 3}-Hypergraphs - Bai, Shuliang; Lu, Linyuan (The Electronic Journal of Combinatorics, 2021)
We consider the Turán problems of 2-edge-colored graphs. A 2-edge-colored graph H=(V, E_r, E_b) is a triple consisting of the vertex set V, the set of red edges E_r and the set of blue edges E_b where E_r and E_b do not have to be disjoint. The Turán density π(H) of H is defined to be _n→∞ _G_nh_n(G_n), where G_n is chosen among all possible 2-edge-colored graphs on n vertices containing no H as a sub-graph and h_n(G_n)=(|E_r(G)|+|E_b(G)|)/n2 is the formula to measure the edge density of G_n. We will determine the Turán densities of all 2-edge-colored bipartite graphs. We also give an important application on the Turán problems of {2, 3}-hypergraphs.