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arXiv · 1610.04874

Coloring Graphs to Produce Properly Colored Walks

Robert Melville·Wayne Goddard
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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.

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Robert Melville, Wayne Goddard. 2017-04-21. Coloring Graphs to Produce Properly Colored Walks. https://arxiv.org/abs/1610.04874

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