Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
NP-hard graph problems and boundary classes of graphs
Theoretical Computer Science
Boundary classes of planar graphs
Combinatorics, Probability and Computing
Recent developments on graphs of bounded clique-width
Discrete Applied Mathematics
A Complete Characterisation of the Linear Clique-Width of Path Powers
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Tree-width and optimization in bounded degree graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Colouring vertices of triangle-free graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On the complexity of the dominating induced matching problem in hereditary classes of graphs
Discrete Applied Mathematics
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Exploiting restricted linear structure to cope with the hardness of clique-width
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Colouring of graphs with Ramsey-type forbidden subgraphs
Theoretical Computer Science
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The band-, tree-, and clique-width are of primary importance in algorithmic graph theory due to the fact that many problems that are NP-hard for general graphs can be solved in polynomial time when restricted to graphs where one of these parameters is bounded. It is known that for any fixed $\Delta \geq 3$, all three parameters are unbounded for graphs with vertex degree at most $\Delta$. In this paper, we distinguish representative subclasses of graphs with bounded vertex degree that have bounded band-, tree-, or clique-width. Our proofs are constructive and lead to efficient algorithms for a variety of NP-hard graph problems when restricted to those classes.