No antitwins in minimal imperfect graphs
Journal of Combinatorial Theory Series B
Discrete Mathematics - Special issue on graph theory and applications
Graph classes: a survey
Dynamic Programming on Distance-Hereditary Graphs
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Graphs of bounded rank-width
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Combinatorial Algorithms
Characterisations and linear-time recognition of probe cographs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Classifying rankwidth k-DH-graphs
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Black-and-white threshold graphs
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Black-and-white threshold graphs
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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The $\mathcal{G}$-width of a class of graphs $\mathcal{G}$ is defined as follows. A graph G has $\mathcal{G}$-width k if there are k independent sets ℕ1,...,ℕk in G such that G can be embedded into a graph $H \in \mathcal{G}$ such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in ℕi. For the class $\mathfrak{C}$ of cographs we show that $\mathfrak{C}$-width is NP-complete. We show that the recognition is fixed-parameter tractable, and we show that there exists a finite obstruction set. We introduce simple-width as an alternative for rankwidth and we characterize the graphs with simple-width at most two.