### Abstract

Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let ϕ(n, H) be the smallest number ϕ such that any graph G of order n admits an H-decomposition with at most ϕ parts. Pikhurko and Sousa conjectured that ϕ(n, H)=ex(n, H) for X(H) ≥ 3 and all sufficiently large n, where ex(n, H) denotes the maximum number of edges in a graph on n vertices not containing H as a subgraph. Their conjecture has been verified by Özkahya and Person for all edge-critical graphs H. In this article, the conjecture is verified for the k-fan graph. The k-fan graph, denoted byF_{k}, is the graph on 2k+1 vertices consisting of k triangles that intersect in exactly one common vertex called the center of the k-fan.

Original language | English |
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Pages (from-to) | 400-411 |

Number of pages | 12 |

Journal | Journal Of Graph Theory |

Volume | 85 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2017 |

### Keywords

- extremal graph
- fan graph
- graph decomposition