<?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%">Pikhurko, Oleg</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%">Minimum H-Decompositions of Graphs</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Combinatorial Theory, B</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S009589560700038X</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/tmjs/files/h_decomposition.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">97</style></volume><pages><style face="normal" font="default" size="100%">1041–1055</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Given 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 φH(n) be the smallest number φ such that every graph G of order n admits an H-decomposition with at most φ parts. In the paper it is proved that φH(n)=tr−1(n)+o(n2) for every graph H of chromatic number r≥3, where tr(n) is the maximum size of an r-partite graph of order n. Moreover, when H is bipartite, the authors determine φH(n) with a constant additive error.&lt;/p&gt;
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