Graph Coloring Algorithms

Graph coloring is a fundamental problem which often appears in various scheduling problems like the file transfer problem on computer networks. In this paper we survey recent advances and results on the edge-coloring the /-coloring the [g f]-coloring and the total coloring problem for various classes of graphs such as bipartite graphs series-parallel graphs planar graphs and graphs having fixed degeneracy tree-width genus arboricity unicyclic index or thickness. In particular we review various upper bounds on the minimum numbers of colors required to color these classes of graphs and present efficient sequential and parallel algorithms to find colorings of graphs with these numbers of colors.