A note on bipartite subgraphs of triangle‐free graphs

  • Authors:
  • James B. Shearer

  • Affiliations:
  • IBM Research Division, T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 1992

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Abstract

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.