Testing subgraphs in large graphs

  • Authors:
  • Noga Alon

  • Affiliations:
  • Schools of Mathematics and Computer Science, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel

  • Venue:
  • Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
  • Year:
  • 2002

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Abstract

Let H be a fixed graph with h vertices, let G be a graph on n vertices, and suppose that at least εn2 edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f(ε, H)nh copies of H. We show that the largest possible function f(ε, H) is polynomial in ε if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1/ε, if and only if H is bipartite.