Greedy -colorings of graphs

This paper deals with greedy T -colorings of graphs, i.e.  T -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 T -colorings have three nice properties: ( 1 ) their span and edge span are equal; ( 2 ) the number of colors they use is independent of T ; ( 3 ) the set of colors they use is a function of T and the number of colors used, only. As a result of these considerations we receive some necessary and sufficient conditions for a greedy T -coloring to be optimal. The paper ends with some considerations concerning greedy algorithms with color interchange.