<?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%">The H-Decomposition Problem for Graphs</style></title><secondary-title><style face="normal" font="default" size="100%">Applied Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.scirp.org/journal/am/</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/tmjs/files/2012-h-decomp-problem.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">3</style></volume><pages><style face="normal" font="default" size="100%">1719-1722</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The concept of H-decompositions of graphs was first introduced by Erdös, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. 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 Ф(n,H) be the smallest number Ф, such that, any graph of order n admits an H-decomposition with at most Ф parts. The exact computation of Ф(n,H) for an arbitrary H is still an open problem. Recently, a few papers have been published about this problem. In this survey we will bring together all the results about H-decompositions. We will also introduce two new related problems, namely Weighted H-Decompositions of graphs and Monochromatic H-Decompositions of graphs.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">11</style></issue></record></records></xml>