Proper Connection with Many Colors
Journal of Combinatorics
We say an edge-colored graph is properly connected if, between every pair of vertices, there exists a properly colored path. For a graph G, define the proper connection number pc(G) to be the minimum number of colors k such that there exists a k-coloring of E(G) which is properly connected. In this work, we study conditions on G which force upper bounds on pc(G).
Fujita, Shinya, Aydin Gerek, Colton Magnant.
"Proper Connection with Many Colors."
Journal of Combinatorics, 3 (4): 683-693.