Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776782 | Discrete Mathematics | 2017 | 5 Pages |
Abstract
An edge-coloured graph G is called properly connected if any two vertices are connected by a path whose edges are properly coloured. The proper connection number of a connected graph G, denoted by pc(G), is the smallest number of colours that are needed in order to make G properly connected. Our main result is the following: Let G be a connected graph of order n and kâ¥2. If |E(G)|â¥nâkâ12+k+2, then pc(G)â¤k except when k=2 and Gâ{G1,G2}, where G1=K1â¨(2K1+K2) and G2=K1â¨(K1+2K2).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Susan A. van Aardt, Christoph Brause, Alewyn P. Burger, Marietjie Frick, Arnfried Kemnitz, Ingo Schiermeyer,