<?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%">Pikhurko O.</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%">Monochromatic Clique 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%">2015</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/tmjs/files/general-mono-clique.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">80</style></volume><pages><style face="normal" font="default" size="100%">287-298</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A \emph{monochromatic $\mathcal H$-decomposition} of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every&lt;br /&gt;
order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa [``Monochromatic $K_r$-decompositions of graphs&quot;, \emph{Journal of Graph Theory}76:89-100,2014], we solve this problem&lt;br /&gt;
when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.&lt;/p&gt;
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