Proper Connection of Graphs

Authors

Valentin Borozan, University Paris
Shinya Fujita, Maebashi Institute of TechnologyFollow
Aydin Gerek, Lehigh UniversityFollow
Colton Magnant, Georgia Southern UniversityFollow
Yannis Manoussakis, University Paris
Leandro Montero, University Paris
Zsolt Tuza, University of PannoniaFollow

Document Type

Article

Publication Date

9-6-2012

Publication Title

Discrete Mathematics

DOI

10.1016/j.disc.2011.09.003

ISSN

0012-365X

Abstract

An edge-colored graph G is k-proper connected if every pair of vertices is connected by k internally pairwise vertex-disjoint proper colored paths. The k-proper connection number of a connected graph G, denoted by pc_k(G), is the smallest number of colors that are needed to color the edges of G in order to make it k-proper connected. In this paper we prove several upper bounds for pc_k(G). We state some conjectures for general and bipartite graphs, and we prove them for the case when k=1. In particular, we prove a variety of conditions on G which imply pc₁(G)=2.

Recommended Citation

Borozan, Valentin, Shinya Fujita, Aydin Gerek, Colton Magnant, Yannis Manoussakis, Leandro Montero, Zsolt Tuza. 2012. "Proper Connection of Graphs." Discrete Mathematics, 312 (17): 2550-2560. doi: 10.1016/j.disc.2011.09.003
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/105