### 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 1 1965 |

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### ASJC Scopus subject areas

- Mathematics(all)