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

Copyright

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