A note on bipartite subgraphs of triangle-free graphs

Let G be a triangle-free graph on n points with m edges and vertex degrees d₁, d₂,…, d_n. Let k be the maximum number of edges in a bipartite subgraph of G. In this note we show that k ? m/2 + Σ √d_i. It follows as a corollary that k ? m/2 + cm^3/4.