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,…, dn. Let k be the maximum number of edges in a bipartite subgraph of G. In this note we show that k ⩾ m/2 + Σ **image** √di. It follows as a corollary that k ⩾ m/2 + cm3/4. © 1992 Wiley Periodicals, Inc.