Abstract

An edge-colored directed graph is called properly connected if, between every pair of vertices, there is a properly colored directed path. We study some conditions on directed graphs which guarantee the existence of a coloring that is properly connected. We also study conditions on a colored directed graph which guarantee that the coloring is properly connected.

Keywords: directed graph; edge coloring; proper connection

MSC: 05C15, 05C20

Pages:  58$-$65     

Volume  68 ,  Issue  1 ,  2016