On clique‐inverse graphs of graphs with bounded clique number

Colouring perfect graphs with bounded clique number

A graph is perfect if the chromatic number of every induced subgraph equals the size of its largest clique, and an algorithm of Grötschel, Lovász, and Schrijver [9] from 1988 finds an optimal colouring of a perfect graph in polynomial time. But this algorithm uses the ellipsoid method, and it is a well-known open question to construct a “combinatorial” polynomial-time algorithm that yields an o...

Multicut on Graphs of Bounded Clique-Width

Several variants of Multicut problems arise in applications like circuit and network design. In general, these problems are NP-complete. The goal of our work is to investigate the potential of clique-width for identifying tractable fragments of Multicut. We show for several parameterizations involving clique-width whether they lead to tractability or not. Since bounded tree-width implies bounde...

Graph Operations on Clique-Width Bounded Graphs

In this paper we survey the behavior of various graph operations on the graph parameters clique-width and NLC-width. We give upper and lower bounds for the clique-width and NLC-width of the modi ed graphs in terms of the clique-width and NLC-width of the involved graphs. Therefor we consider the binary graph operations join, co-join, sum, di erence, products, corona, substitution, and 1-sum, an...

Searching Graphs with Large Clique Number

Graphs of small bounded linear clique-width

In this paper we give the first characterisation of graphs with linear clique-width at most 3, and we give a polynomial-time recognition algorithm for such graphs. In addition, we give a new characterisation of graphs with linear clique-width at most 2 and a new layout characterisation of linear clique-width in general. Among our results is also a decomposition scheme that preserves the linear ...