
Graph Isomorphism for (H_1,H_2)free Graphs: An Almost Complete Dichotomy
We consider the Graph Isomorphism problem for classes of graphs characte...
read it

Bounding the MimWidth of Hereditary Graph Classes
A large number of NPhard graph problems become polynomialtime solvable...
read it

CliqueWidth for Hereditary Graph Classes
Cliquewidth is a wellstudied graph parameter owing to its use in under...
read it

On the CliqueWidth of Unigraphs
Cliquewidth is a wellstudied graph parameter. For graphs of bounded cl...
read it

Cliquewidth and WellQuasiOrdering of TriangleFree Graph Classes
Daligault, Rao and Thomassé asked whether every hereditary graph class t...
read it

A unified algorithm for colouring graphs of bounded cliquewidth
Cliquewidth is one of the graph complexity measures leading to polynomi...
read it

Colouring SquareFree Graphs without Long Induced Paths
The complexity of Colouring is fully understood for Hfree graphs, but ...
read it
CliqueWidth: Harnessing the Power of Atoms
Many NPcomplete graph problems are polynomially solvable on graph classes of bounded cliquewidth. Several of these problems are polynomially solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cutset) of G. Hence, we initiate a systematic study into boundedness of cliquewidth of atoms of hereditary graph classes. A graph G is Hfree if H is not an induced subgraph of G, and G is (H_1, H_2)free if it is both H_1free and H_2free. A class of Hfree graphs has bounded cliquewidth if and only if its atoms have this property. This is no longer true for (H_1, H_2)free graphs as evidenced by one known example. We prove the existence of another such pair (H_1, H_2) and classify the boundedness of (H_1, H_2)free atoms for all but 22 cases.
READ FULL TEXT
Comments
There are no comments yet.