On a probabilistic method in graph theory

Abstract We show that a simple graph U is edge-transitive if and only if it has the property that for any subgraphs G and H of U , there is a subgraph G 1 of G , isomorphic to a subgraph of H , with |E(G 1 )|⩾ E(G)|·|E(H)| |E(U)| , where | E ( K )| denotes the number of edges of a graph K .