Partitioning the flags of PG(2, q) into strong representative systems

In this paper we show a natural extension of the idea used by Illés, Szőnyi and Wettl which proved that the flags of PG(2, q) can be partitioned into (q−1) √ q+3q strong representative systems for q an odd square. From a generalization of the Buekenhout construction of unitals their idea can be applied for any non-prime q to yield that q +2q strong representative systems partition the flags of PG(2, q). In this way we also give a solution to a question of Gyárfás about the strong chromatic index of the bipartite graph corresponding to PG(2, q), for q