### Abstract

The author proves that if C is a sufficiently large constant then every graph of n vertices and [Cn^{ 3/2}] edges contains a hexagon X_{ 1}, X_{ 2}, X_{ 3}, X_{ 4}, X_{ 5}, X_{ 6} and a seventh vertex Y joined to X_{ 1}, X_{ 3} and X_{ 5}. The problem is left open whether our graph contains the edges of a cube, (i.e. an eight vertex Z joined to X_{ 2}, X_{ 4} and X_{ 6}).

Original language | English |
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Pages (from-to) | 113-116 |

Number of pages | 4 |

Journal | Israel Journal of Mathematics |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1965 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On some extremal problems in graph theory.** / Erdős, P.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 3, no. 2, pp. 113-116. https://doi.org/10.1007/BF02760037

}

TY - JOUR

T1 - On some extremal problems in graph theory

AU - Erdős, P.

PY - 1965/6

Y1 - 1965/6

N2 - The author proves that if C is a sufficiently large constant then every graph of n vertices and [Cn 3/2] edges contains a hexagon X 1, X 2, X 3, X 4, X 5, X 6 and a seventh vertex Y joined to X 1, X 3 and X 5. The problem is left open whether our graph contains the edges of a cube, (i.e. an eight vertex Z joined to X 2, X 4 and X 6).

AB - The author proves that if C is a sufficiently large constant then every graph of n vertices and [Cn 3/2] edges contains a hexagon X 1, X 2, X 3, X 4, X 5, X 6 and a seventh vertex Y joined to X 1, X 3 and X 5. The problem is left open whether our graph contains the edges of a cube, (i.e. an eight vertex Z joined to X 2, X 4 and X 6).

UR - http://www.scopus.com/inward/record.url?scp=51249166833&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249166833&partnerID=8YFLogxK

U2 - 10.1007/BF02760037

DO - 10.1007/BF02760037

M3 - Article

AN - SCOPUS:51249166833

VL - 3

SP - 113

EP - 116

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 2

ER -