### 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 E_{1},..., E_{i} and the edge set E(H) of H can be partitioned into E_{1},..., E_{i} in such a way that for each i, the graphs formed by E_{i} and E_{i}^{′} are isomorphic.

Original language | English (US) |
---|---|

Pages (from-to) | 248-260 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - 1985 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory, Series B*,

*38*(3), 248-260. https://doi.org/10.1016/0095-8956(85)90070-X

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

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series B*, vol. 38, no. 3, pp. 248-260. https://doi.org/10.1016/0095-8956(85)90070-X

}

TY - JOUR

T1 - Extremal subgraphs for two graphs

AU - Chung, F. R K

AU - Erdös, P.

AU - Spencer, J.

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

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U2 - 10.1016/0095-8956(85)90070-X

DO - 10.1016/0095-8956(85)90070-X

M3 - Article

VL - 38

SP - 248

EP - 260

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 3

ER -