Title

Proper Connection of Graphs

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 pck(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 pck(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.

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