%0 Journal Article %T An exact value for the path-chromatic index of a complete graph %A Frank Harary %A £¿solt Tuza %J Le Matematiche %D 1989 %I University of Catania %X We prove that the edge of Kn cannot be partitioned into less than (n-1)/t Pi+2-free subgraphs. We show that this inequality is sharp and characterize the edge partitions which attain it. In the process, we point out a surprising connection between the combinatorial designs and the conditional chromatic index. %U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/691