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Combinatorica

, Volume 18, Issue 1, pp 101–120 | Cite as

An Extremal Problem For Random Graphs And The Number Of Graphs With Large Even-Girth

  • Y. Kohayakawa
  • B. Kreuter
  • A. Steger
Original Paper

C

2 k -free subgraph of a random graph \(\) may have, obtaining best possible results for a range of p=p(n). Our estimates strengthen previous bounds of Füredi [12] and Haxell, Kohayakawa, and Łuczak [13]. Two main tools are used here: the first one is an upper bound for the number of graphs with large even-girth, i.e., graphs without short even cycles, with a given number of vertices and edges, and satisfying a certain additional pseudorandom condition; the second tool is the powerful result of Ajtai, Komlós, Pintz, Spencer, and Szemerédi [1] on uncrowded hypergraphs as given by Duke, Lefmann, and Rödl [7].

AMS Subject Classification (1991) Classes:  05A16, 05C35, 05C38, 05C80 

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Copyright information

© János Bolyai Mathematical Society, 1998

Authors and Affiliations

  • Y. Kohayakawa
    • 1
  • B. Kreuter
    • 2
  • A. Steger
    • 3
  1. 1.Instituto de Matemática e Estatística, Universidade de São Paulo; Rua do Matão 1010, 05508–900 São Paulo, Brazil; E-mail: yoshi@ime.usp.brBR
  2. 2.Institut für Informatik, Humboldt Universität zu Berlin; Unter den Linden 6, 10099 Berlin, Germany; E-mail: kreuter@informatik.hu-berlin.deDE
  3. 3.Institut für Informatik, Technische Universität München; 80290 München, Germany; E-mail: steger@informatik.tu-muenchen.deDE

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