@techreport{TR-IC-09-19, number = {IC-09-19}, author = {Vagner Pedrotti and CĂ©lia Picinin de Mello}, title = {{$K_r$}-packing of {$P_4$}-tidy graphs}, month = {May}, year = {2009}, institution = {Institute of Computing, University of Campinas}, note = {In English, 11 pages. \par\selectlanguage{english}\textbf{Abstract} The $K_r$-packing problem asks for the maximum number of pairwise vertex-disjoint cliques of size $r$ in a graph, for a fixed integer $r \geq 2$. This problem is NP-hard for general graphs when $r \geq 3$, and even when restricted to chordal graphs. However, Guruswami et al. proposed a polynomial-time algorithm for cographs (when $r$ is fixed). In this work we extended this algorithm to $P_4$-tidy graphs, keeping the same time complexity. } }