Thoroughly Dispersed Colorings

Abstract

We consider (not necessarily proper) colorings of the vertices of a graph where every color is thoroughly dispersed, that is, appears in every open neighborhood. Equivalently, every color is a total dominating set. We define td(G) as the maximum number of colors in such a coloring and FTD(G) as the fractional version thereof. In particular, we show that… (More)

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