“…For convenience, we represent an edge {a, b} by ab. Our consideration on 2-colored graphs is motivated by the study of Turán density of non-uniform hypergraphs, which was first introduced by Johnston and Lu [10], then studied by us [3]. We refer a non-uniform hypergraph H as R-graph, where R is the set of all the cardinalities of edges in H. For example, H is a hypergraph on vertices {1, 2, 3, 4} with edges {1}, {2, 3} and {1, 2, 4}, then the edge type of H is R(H) = {1, 2, 3} as the cardinalities of all edges are 1, 2, 3.…”