Coloring Graphs to Produce Properly Colored Walks
Combinatorics
2017-04-25 v2
Abstract
For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair of vertices without two consecutive edges having the same color. We show that the proper-walk connection number is at most three for all cyclic graphs, and at most two for bridgeless graphs. We also characterize the bipartite graphs that have proper-walk connection number equal to two, and show that this characterization also holds for the analogous problem where one is restricted to properly colored paths.
Cite
@article{arxiv.1610.04874,
title = {Coloring Graphs to Produce Properly Colored Walks},
author = {Robert Melville and Wayne Goddard},
journal= {arXiv preprint arXiv:1610.04874},
year = {2017}
}