On the number of edge disjoint cliques in graphs of given size

Abstract

In this paper, we prove that any graph ofn vertices andt r−1(n)+m edges, wheret r−1(n) is the Turán number, contains (1−o(1)m edge disjointK r'sifm=o(n 2). Furthermore, we determine the maximumm such that every graph ofn vertices andt r−1(n)+m edges containsm edge disjointK r's ifn is sufficiently large.

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Research partially supported by Hungarian National Foundation for Scientific Research Grant no. 1812.

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Győri, E. On the number of edge disjoint cliques in graphs of given size. Combinatorica 11, 231–243 (1991). https://doi.org/10.1007/BF01205075

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AMS code classification (1980)

  • 05 C 35