- Citation:
- Liu, H., and Teresa Sousa. "Fan Decompositions of Graphs." Journal of Graph Theory (In Press).

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 f(n;H) be the smallest number such that any graph

G of order n admits an H-decomposition with at most f(n;H) parts. Pikhurko and

Sousa conjectured that f(n;H) = ex(n;H) for (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 veried by

Ozkahya and Person for all edge-critical graphs H. In this article, the conjecture

is veried for the k-fan graph. The k-fan graph, denoted by F_k, is the graph on

2k + 1 vertices consisting of k triangles which intersect in exactly one common

vertex called the centre of the k-fan.