Extremal subgraphs for two graphs

F. R K Chung, P. Erdös, J. Spencer

Research output: Contribution to journalArticle

Abstract

In this paper we study several interrelated extremal graph problems: 1. (i) Given integers n, e, m, what is the largest integer f(n, e, m) such that every graph with n vertices and e edges must have an induced m-vertex subgraph with at least f(n, e, m) edges? 2. (ii) Given integers n, e, e′, what is the largest integer g(n, e, e′) such that any two n-vertex graphs G and H, with e and e′ edges, respectively, must have a common subgraph with at least g(n, e, e′) edges? Results obtained here can be used for solving several questions related to the following graph decomposition problem, previously studied by two of the authors and others. 3. (iii) Given integers n, r, what is the least integer t = U(n, r) such that for any two n-vertex r-uniform hypergraphs G and H with the same number of edges the edge set E(G) of G can be partitioned into E1,..., Ei and the edge set E(H) of H can be partitioned into E1,..., Ei in such a way that for each i, the graphs formed by Ei and Ei are isomorphic.

Original languageEnglish (US)
Pages (from-to)248-260
Number of pages13
JournalJournal of Combinatorial Theory, Series B
Volume38
Issue number3
DOIs
StatePublished - 1985

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Subgraph
Decomposition
Integer
Graph in graph theory
Vertex of a graph
Graph Decomposition
Extremal Graphs
Uniform Hypergraph
Isomorphic

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Extremal subgraphs for two graphs. / Chung, F. R K; Erdös, P.; Spencer, J.

In: Journal of Combinatorial Theory, Series B, Vol. 38, No. 3, 1985, p. 248-260.

Research output: Contribution to journalArticle

Chung, F. R K ; Erdös, P. ; Spencer, J. / Extremal subgraphs for two graphs. In: Journal of Combinatorial Theory, Series B. 1985 ; Vol. 38, No. 3. pp. 248-260.
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