The complexity analysis of the edge-ranking problem for hereditary graph classes with at most three prohibitions

We completely characterize all hereditary classes defined by at most three forbidden induced subgraphs (obstructions) for which the edge list-ranking problem is polynomial-time solvable. For each class in this family, the algorithm of determining the complexity status of the problem in the class is based on checking whether or not the obstructions belong to some special (“critical”) classes of graphs. The family of such special classes includes, in particular, inclusionwise minimal classes for which the problem is NP-complete. All classes of this type defined by at most three obstructions are described. Ill. 4, bibliogr. 14.