On a Turán type problem of Erdös

Abstract

Let Lk be the graph formed by the lowest three levels of the Boolean lattice B k , i.e.,V(Lk)={0, 1,...,k, 12, 13,..., (k−1)k} and 0is connected toi for all 1≤ik, andij is connected toi andj (1≤i<jk).

It is proved that if a graph G overn vertices has at leastk 3/2 n 3/2 edges, then it contains a copy of Lk.

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Research supported in part by the Hungarian National Science Foundation under Grant No. 1812

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Füredi, Z. On a Turán type problem of Erdös. Combinatorica 11, 75–79 (1991). https://doi.org/10.1007/BF01375476

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 65