Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
Treewidth for graphs with small chordality
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Graph classes: a survey
Covering edges by cliques with regard to keyword conflicts and intersection graphs
Communications of the ACM
Minimal Triangulations for Graphs with "Few" Minimal Separators
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Journal of Computer and System Sciences
Data reduction and exact algorithms for clique cover
Journal of Experimental Algorithmics (JEA)
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Every graph is the edge intersection graph of subtrees of a tree. The tree-degree of a graph is the minimum maximal degree of the underlying tree for which there exists a subtree intersection model. Computing the tree-degree is NP-complete even for planar graphs, but polynomial time algorithms exist for outer-planar graphs, diamond-free graphs and chordal graphs. The number of minimal separators of graphs with bounded tree-degree is polynomial. This implies that the treewidth of graphs with bounded tree-degree can be computed efficiently, even without the model given in advance.