A (proper) coloring of a finite simple graph (G) is pe#ect if it uses exactly o(G) colors, where o(G) denotes the order of a largest clique in G. A coloring is locally-perfect [3] if it induces on the neighborhood of every vertex v a perfect coloring of this neighborhood. A graph G is perfect (resp. locally-petfect) if every induced subgraph admits a perfect (resp. locally-perfect) coloring. Pr...

Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs, where the former admits polynomia...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs....

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in nding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. W...

We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.

A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least 5 or the complement of one. The “strong perfect graph conjecture” (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by C...

The circular arc coloring problem is to find a minimum coloring of a set of arcs of a circle so that no two overlapping arcs share a color. This N P-hard problem arises in a rich variety of applications and has been studied extensively. In this paper we present an O(n2m) combinatorial algorithm for optimally coloring any set of arcs that corresponds to a perfect graph, and propose a new approac...

We consider the question of the computational complexity of coloring perfect graphs with some precolored vertices. It is well known that a perfect graph can be colored optimally in polynomial time. Our results give a sharp border between the polynomial and NP-complete instances, when precolored vertices occur. The key result on the polynomially solvable cases includes a good characterization th...