We bound the clique width of a graph in terms of its tree width on the one hand, and of its edge complement on the other, and investigate alternate hierarchical decompositions that apply to wider classes of graphs.Expand

This chapter presents three mathematical tools that can be used to describe graph-grammars and the sets generated by them and presents a comparison of the powers of several logical languages.Expand

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements.Expand

We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with ``too many'' induced paths with four vertices.Expand

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

A synthesis of various aspects of infinite trees, invcstigatcd bc diIlt*ic*nt ,tuthor\ III differenr contlbxts and hopes to he a unifying step towards a theor! of infinite trct.s.Expand

Graphs are finite and handled as relational structures. We give some answers to the following general questions:
1.
(1) For which classes of graphs C is it possible to specify a linear ordering of… Expand

Abstract In every undirected graph or, more generally, in every hypergraph of bounded rank, one can specify an orientation of the edges or hyperedges by monadic second-order formulas using quantifications on sets of edges or Hyperedges.Expand