Rational exponents in extremal graph theory

  • Boris Bukh

    Carnegie Mellon University, Pittsburgh, USA
  • David Conlon

    University of Oxford, UK


Given a family of graphs , the extremal number ex is the largest for which there exists a graph with vertices and edges containing no graph from the family as a subgraph. We show that for every rational number between 1 and 2, there is a family of graphs such that ex. This solves a longstanding problem in the area of extremal graph theory.

Cite this article

Boris Bukh, David Conlon, Rational exponents in extremal graph theory. J. Eur. Math. Soc. 20 (2018), no. 7, pp. 1747–1757

DOI 10.4171/JEMS/798