Packing of two digraphs into a transitive tournament Original Research Article

Let image and image be two oriented graphs of order n without directed cycles. Görlich, Pilśniak and Woźniak proved [A note on a packing problem in transitive tournaments, preprint Faculty of Applied Mathematics, AGH University of Science and Technology, No. 37/2002] that if the number of arcs in image is sufficiently small (not greater than image) then two copies of image are packable into the transitive tournament image. This bound is best possible. In this paper we give a generalization of this result. We show that if the sum of sizes of image and image is not greater than image then the digraphs image and image are packable into image.