Abstract
AbstractGiven 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 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 for and all sufficiently large n, where 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 by , is the graph on vertices consisting of k triangles that intersect in exactly one common vertex called the center of the k‐fan.
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