<?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%">Sousa, Teresa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Friendship decompositions of graphs</style></title><secondary-title><style face="normal" font="default" size="100%">Discrete Mathemathics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S0012365X07004876</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/tmjs/files/friendship-decomposition.pdf</style></url></related-urls></urls><number><style face="normal" font="default" size="100%">15</style></number><volume><style face="normal" font="default" size="100%">308</style></volume><pages><style face="normal" font="default" size="100%">3352–3360</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let G be a simple graph. A clique is a subgraph of G isomorphic to a complete graph, and a t-friendship graph is a graph consisting of t edge-disjoint cliques sharing one vertex. A t-friendship decomposition of G for a fixed value of t is a set F of edge-disjoint t-friendship subgraphs of G such that every edge of G belongs to exactly one element of F. It is proved that any graph of order n admits a t-friendship decomposition with at most n2/4t+n/4t+n elements for all fixed t≥2. For t=2,3 exact bounds are given. For t=2 the bound is ⌈n2/8⌉ for n even and (n2−1)/8 for n odd; for t=3 the bound is ⌈n2/12⌉ for n even and ⌈(n2−1)/12⌉ for n odd. &lt;/p&gt;
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