### Abstract

P. Turán has asked the following question:. Let I^{12} be the graph determined by the vertices and edges of an icosahedron. What is the maximum number of edges of a graph G^{n} of n vertices if G^{n} does not contain I^{12} as a subgraph? We shall answer this question by proving that if n is sufficiently large, then there exists only one graph having maximum number of edges among the graphs of n vertices and not containing I^{12}. This graph H^{n} can be defined in the following way:. Let us divide n - 2 vertices into 3 classes each of which contains [ (n-2) 3] or [ (n-2) 3] + 1 vertices. Join two vertices iff they are in different classes. Join two vertices outside of these classes to each other and to every vertex of these three classes.

Original language | English |
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Pages (from-to) | 69-79 |

Number of pages | 11 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 17 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1974 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics