<?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%">Decompositions of graphs into a given clique-extension</style></title><secondary-title><style face="normal" font="default" size="100%">Ars Combinatoria</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.combinatorialmath.ca/arscombinatoria/vol100.html</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/tmjs/files/2011-04-clique_extension.pdf</style></url></related-urls></urls><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">100</style></volume><pages><style face="normal" font="default" size="100%">465–472</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;For r≥3, a clique-extension of order r+1 is a connected graph that consists of a Kr  plus another vertex adjacent to at most r-1 vertices of Kr. In this paper we consider the problem of finding the smallest number t such that any graph G of order n admits a decomposition into  edge disjoint copies of a fixed graph H and single edges with at most t elements.  Here we solve the case when H is a fixed clique-extension of order r+1, for all r≥3 and will also obtain all extremal graphs. This work extends results proved by Bollobás [Math.\ Proc.\ Cambridge Philosophical Soc 79 (1976) 19--24]  for cliques.&lt;/p&gt;
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