### Abstract

Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (^{k}_{2}) - 1 is the famous result of Turán.

Original language | English |
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Pages (from-to) | 185-207 |

Number of pages | 23 |

Journal | Journal of Graph Theory |

Volume | 29 |

Issue number | 3 |

Publication status | Published - Nov 1998 |

### Fingerprint

### Keywords

- Dirac's Theorem
- Extremal graphs
- Turán's Theorem

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*29*(3), 185-207.

**Extremal Graphs with Bounded Densities of Small Subgraphs.** / Griggs, Jerrold R.; Simonovits, M.; Thomas, George Rubin.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 29, no. 3, pp. 185-207.

}

TY - JOUR

T1 - Extremal Graphs with Bounded Densities of Small Subgraphs

AU - Griggs, Jerrold R.

AU - Simonovits, M.

AU - Thomas, George Rubin

PY - 1998/11

Y1 - 1998/11

N2 - Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (k2) - 1 is the famous result of Turán.

AB - Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (k2) - 1 is the famous result of Turán.

KW - Dirac's Theorem

KW - Extremal graphs

KW - Turán's Theorem

UR - http://www.scopus.com/inward/record.url?scp=0032346396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032346396&partnerID=8YFLogxK

M3 - Article

VL - 29

SP - 185

EP - 207

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -