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math.CO2025
All--Isolation in Trees
Geoffrey Boyer, Garrett C. Farrell, Wayne Goddard
We define an all--isolating set of a graph to be a set of vertices such that, if one removes and all its neighbors, then no component in what remains has order or mo…
math.CO2025
A Note on Distance-Fall Colorings
Wayne Goddard, Sonwabile Mafunda
We say a proper coloring of a graph is distance- fall if every vertex is within distance of at least one vertex of every color. We show that if is a connected graph of 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…