Modular decomposition is a technique that applies to (but is not restricted to) graphs. The
notion of a module naturally appears in the proofs of many graph theoretical theorems …

When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are
several types of hierarchical decompositions. Tree decompositions are the best known ones …

Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP
complete problems have linear complexity on graphs with tree-decompositions of bounded …

A module of an undirected graph is a set X of nodes such for each node x not in X, either
every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical …

By making use of lexicographic breadth first search, Lex-BFS and partition refinement with
pivots, we obtain very simple algorithms for some well-known problems in graph theory. We …

Modular decomposition is fundamental for many important problems in algorithmic graph
theory including transitive orientation, the recognition of several classes of graphs, and …

List partitions generalize list colorings and list homomorphisms.(We argue that they may be
called list" semihomomorphisms.") Each symmetric matrix M over 0, 1,* defines a list partition …

The graph invariant twin-width was recently introduced by Bonnet, Kim, Thomassé, and
Watrigan. Problems expressible in first-order logic, which includes many prominent NP-hard …

In this paper, we describe a new simple linear time algorithm to recognize cographs.
Cographs are exactly the P4-free graphs (where P4 denotes the path with 4 vertices). The …