DeepAI AI Chat
Log In Sign Up

A unified algorithm for colouring graphs of bounded clique-width

by   Bruno Courcelle, et al.

Clique-width is one of the graph complexity measures leading to polynomial special-case algorithms for generally NP-complete problems, e.g. graph colourability. The best two currently known algorithms for verifying c-colourability of graphs represented as clique-width terms are optimised towards two different extreme cases, a constant number of colours and a very large number of colours. We present a way to unify these approaches in a single relatively simple algorithm that achieves the state of the art complexity in both cases. The unified algorithm also provides a speed-up for a large number of colours.


page 1

page 2

page 3

page 4


Maximizing Happiness in Graphs of Bounded Clique-Width

Clique-width is one of the most important parameters that describes stru...

The Algorithmic Complexity of Tree-Clique Width

Tree-width has been proven to be a useful parameter to design fast and e...

Graph Isomorphism for (H_1,H_2)-free Graphs: An Almost Complete Dichotomy

We consider the Graph Isomorphism problem for classes of graphs characte...

Clique-Width of Point Configurations

While structural width parameters (of the input) belong to the standard ...

Hard Optimization Problems have Soft Edges

Finding a Maximum Clique is a classic property test from graph theory; f...

Colouring Square-Free Graphs without Long Induced Paths

The complexity of Colouring is fully understood for H-free graphs, but ...

Bypassing the XOR Trick: Stronger Certificates for Hypergraph Clique Number

Let ℋ(k,n,p) be the distribution on k-uniform hypergraphs where every su...