Kernels by monochromatic paths in image-colored unions of quasi-transitive digraphs Original Research Article

A digraph image is a union of quasi-transitive digraphs if its arcs can be partitioned into sets image and image such that the induced subdigraph image is quasi-transitive. Let image be an image-colored asymmetric union of quasi-transitive digraphs such that every chromatic class is completely included in image for some image and is quasi-transitive. We show that if image does not contain 3-colored triangles (directed cycles and transitive subtournaments of order 3), then image has a kernel by monochromatic directed paths.