Directed proper connection of graphs

Colton Magnant, Patrick Ryan Morley, Sarabeth Porter, Pouria Salehi Nowbandegani, Hua Wang

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.