A polynomial algorithm for the min-cut linear arrangement of trees
Journal of the ACM (JACM)
Min Cut is NP-complete for edge weighted trees
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Computing the bandwidth of interval graphs
SIAM Journal on Discrete Mathematics
Cluster analysis for hypertext systems
SIGIR '93 Proceedings of the 16th annual international ACM SIGIR conference on Research and development in information retrieval
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Graph classes: a survey
Approximating layout problems on random geometric graphs
Journal of Algorithms
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Minimizing Width in Linear Layouts
Proceedings of the 10th Colloquium on Automata, Languages and Programming
A Polyhedral Approach to Planar Augmentation and Related Problems
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Polynomial time algorithms for the MIN CUT problem on degree restricted trees
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Cutwidth I: A linear time fixed parameter algorithm
Journal of Algorithms
Cutwidth II: Algorithms for partial w-trees of bounded degree
Journal of Algorithms
Optimal linear arrangement of interval graphs
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Fixed-parameter algorithms for protein similarity search under mRnA structure constraints
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Computing the cutwidth of bipartite permutation graphs in linear time
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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We give a linear-time algorithm to compute the cutwidth of threshold graphs, thereby resolving the computational complexity of cutwidth on this graph class. Although our algorithm is simple and intuitive, its correctness proof relies on a series of non-trivial structural results, and turns out to be surprisingly complex. Threshold graphs are a well-studied subclass of interval graphs and of split graphs, both of which are unrelated subclasses of chordal graphs. To complement our result, we show that cutwidth is NP-complete on split graphs, and consequently also on chordal graphs. In addition, we show that cutwidth is trivial on proper interval graphs, another subclass of interval graphs. The cutwidth of interval graphs is open, and only very few graph classes are known so far on which polynomial-time cutwidth algorithms exist. Thus we contribute to define the border between graph classes on which cutwidth is polynomially solvable and on which it remains NP-complete.