Greedy TT-colorings of graphs

This paper deals with greedy TT-colorings of graphs, i.e. TT-colorings produced by the greedy (or first-fit) algorithm. We study their parameters, such as the number of colors, the span, the edge span and the values of colors they use. In particular, we show that these TT-colorings have three nice properties: (1)(1) their span and edge span are equal; (2)(2) the number of colors they use is independent of TT; (3)(3) the set of colors they use is a function of TT and the number of colors used, only. As a result of these considerations we receive some necessary and sufficient conditions for a greedy TT-coloring to be optimal. The paper ends with some considerations concerning greedy algorithms with color interchange.