Note on the 3-graph counting lemma

نویسندگان

  • Brendan Nagle
  • Vojtech Rödl
  • Mathias Schacht
چکیده

Szemerédi’s regularity lemma proved to be a powerful tool in extremal graph theory. Many of its applications are based on the so-called counting lemma: if G is a kpartite graph with k-partition V1∪ · · ·∪Vk, |V1| = · · · = |Vk| = n, where all induced bipartite graphs G[Vi, Vj ] are (d, ε)-regular, then the number of k-cliques Kk in G is d( k 2)nk(1± o(1)). Frankl and Rödl extended Szemerédi’s regularity lemma to 3-graphs and Nagle and Rödl established an accompanying 3-graph counting lemma analogous to the graph counting lemma above. In this paper, we provide a new proof of the 3-graph counting lemma.

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عنوان ژورنال:
  • Discrete Mathematics

دوره 308  شماره 

صفحات  -

تاریخ انتشار 2008