Optimal proper connection of graphs
Abstract
An edgecolored graph $G$ is called properly colored if no two adjacent edges share a color in $G$. An edgecolored connected graph $G$ is called properly connected if between every pair of distinct vertices, there exists a path that is properly colored. In this paper, we discuss how to make a connected graph properly connected efficiently. More precisely, we consider the problem to convert a given monochromatic graph into properly connected by recoloring $p$ edges with $q$ colors so that $p+q$ is as small as possible. We discuss how this can be done efficiently for some restricted graphs, such as trees, complete bipartite graphs and graphs with independence number $2$.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.03311
 Bibcode:
 2019arXiv190303311F
 Keywords:

 Mathematics  Combinatorics;
 05C15
 EPrint:
 8 pages