6 citations · 8 across the 7 of their papers we have counts for
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math.CO2016
Coloring Graphs to Produce Properly Colored Walks
Robert Melville, Wayne Goddard
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 o…
math.CO2016★ 6 cited
Thoroughly Distributed Colorings
Wayne Goddard, Michael A. Henning
We consider (not necessarily proper) colorings of the vertices of a graph where every color is thoroughly distributed, that is, appears in every open neighborhood. Equivalently, ev…
math.CO2016★ 1 cited
Vertex Colorings without Rainbow or Monochromatic Subgraphs
Wayne Goddard, Honghai Xu
This paper investigates vertex colorings of graphs such that some rainbow subgraph~ and some monochromatic subgraph are forbidden. Previous work focussed on the case that $R…