### Abstract

The main result of this paper is that for a special, but rather wide class of "sample graphs", the extremal graphs, i.e. the graphs of n vertices without subgraphs isomorphic to the sample graph and having maximum number of edges under this condition, have very simple and symmetric structure. This result remains valid even in the case when the condition "the graph does not contain the sample graph" is replaced by the condition "the graph does not contain the sample graph and its chromatic number is greater than t, where t is a fixed integer". The results of this paper have a lot of different applications, a few of which are listed in Section 3.

Original language | English |
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Pages (from-to) | 349-376 |

Number of pages | 28 |

Journal | Discrete Mathematics |

Volume | 7 |

Issue number | 2 |

Publication status | Published - 1974 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

**Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions.** / Simonovits, M.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 7, no. 2, pp. 349-376.

}

TY - JOUR

T1 - Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions

AU - Simonovits, M.

PY - 1974

Y1 - 1974

N2 - The main result of this paper is that for a special, but rather wide class of "sample graphs", the extremal graphs, i.e. the graphs of n vertices without subgraphs isomorphic to the sample graph and having maximum number of edges under this condition, have very simple and symmetric structure. This result remains valid even in the case when the condition "the graph does not contain the sample graph" is replaced by the condition "the graph does not contain the sample graph and its chromatic number is greater than t, where t is a fixed integer". The results of this paper have a lot of different applications, a few of which are listed in Section 3.

AB - The main result of this paper is that for a special, but rather wide class of "sample graphs", the extremal graphs, i.e. the graphs of n vertices without subgraphs isomorphic to the sample graph and having maximum number of edges under this condition, have very simple and symmetric structure. This result remains valid even in the case when the condition "the graph does not contain the sample graph" is replaced by the condition "the graph does not contain the sample graph and its chromatic number is greater than t, where t is a fixed integer". The results of this paper have a lot of different applications, a few of which are listed in Section 3.

UR - http://www.scopus.com/inward/record.url?scp=0039331474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039331474&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0039331474

VL - 7

SP - 349

EP - 376

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -