On-line coloring of sparse random graphs and random trees

The performance of the greedy coloring algorithm ''first fit'' on sparse random graphs G(n,c/n) and on random trees is investigated. In each case, approximately log(2)log n colors are used, the exact number being concentrated almost surely on at most two consecutive integers for a sparse random graph and on at most three consecutive integers for a random tree. (C) 1997 Academic Press.