On the maximal number of certain subgraphs in Kr-free graphs

Ervin Györi, János Pach, Miklós Simonovits

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Given two graphs H and G, let H(G) denote the number of subgraphs of G isomorphic to H. We prove that if H is a bipartite graph with a one-factor, then for every triangle-free graph G with n vertices H(G) ≤ H(T2(n)), where T2(n) denotes the complete bipartite graph of n vertices whose colour classes are as equal as possible. We also prove that if K is a complete t-partite graph of m vertices, r > t, n ≥ max(m, r - 1), then there exists a complete (r - 1)-partite graph G* with n vertices such that K(G) ≤ K(G*) holds for every Kr-free graph G with n vertices. In particular, in the class of all Kr-free graphs with n vertices the complete balanced (r - 1)-partite graph Tr-1(n) has the largest number of subgraphs isomorphic to Kt (t <r), C4, K2,3. These generalize some theorems of Turán, Erdös and Sauer.

Original languageEnglish
Pages (from-to)31-37
Number of pages7
JournalGraphs and Combinatorics
Volume7
Issue number1
DOIs
Publication statusPublished - Mar 1991

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

On the maximal number of certain subgraphs in Kr-free graphs. / Györi, Ervin; Pach, János; Simonovits, Miklós.

In: Graphs and Combinatorics, Vol. 7, No. 1, 03.1991, p. 31-37.

Research output: Contribution to journalArticle

Györi, Ervin ; Pach, János ; Simonovits, Miklós. / On the maximal number of certain subgraphs in Kr-free graphs. In: Graphs and Combinatorics. 1991 ; Vol. 7, No. 1. pp. 31-37.
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