Résumé : In 2015, El Sahili conjectured that for n ≥ 8, every oriented path of order n is contained in any n-chromatic digraph. After the cases of oriented paths with one and two blocks were solved, the case of three blocks is still open. We treat El Sahili conjecture for paths with three blocks and four blocks by studying the chromatic number that guarantees its existence in the digraph and sometimes by imposing conditions on the structure of the digraph to contain such a path. In our treatment, the tool of maximal forest proved that it is effective and made the problem more flexible. For this reason, light will be shed on this tool showing how it solves the problem by introducing a clear example.
Bio : Maidoun Mortada est enseignante à l’Université Libanaise de Beyrouth et chercheuse au laboratoire Kalma. Elle est en visite au LIB du 5/2 au 19/2.