<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Liu, H.</style></author><author><style face="normal" font="default" size="100%">Sousa, Teresa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Fan Decompositions of Graphs</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Graph Theory</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">In Press</style></year></dates><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Given two graphs G and H, an H-decomposition of G is a partition of the&lt;br /&gt;
edge set of G such that each part is either a single edge or forms a graph&lt;br /&gt;
isomorphic to H. Let f(n;H) be the smallest number  such that any graph&lt;br /&gt;
G of order n admits an H-decomposition with at most f(n;H)  parts. Pikhurko and&lt;br /&gt;
Sousa conjectured that f(n;H) = ex(n;H) for (H)  3 and all sufficiently&lt;br /&gt;
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 veried by&lt;br /&gt;
Ozkahya and Person for all edge-critical graphs H. In this article, the conjecture&lt;br /&gt;
is veried for the k-fan graph. The k-fan graph, denoted by F_k, is the graph on&lt;br /&gt;
2k + 1 vertices consisting of k triangles which intersect in exactly one common&lt;br /&gt;
vertex called the centre of the k-fan.&lt;/p&gt;
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