Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
The question of the exact complexity of solving parity games is one of the major open problems in system verification, as it is equivalent to the problem of model-checking the mod...
Given a graph G we consider the problem of preprocessing it so that given two vertices x,y and a set X of vertices, we can efficiently report the shortest path (or just its length...
Many NP-hard problems can be solved efficiently when the input is restricted to graphs of bounded tree-width or clique-width. In particular, by the celebrated result of Courcelle,...
Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtano...