The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Cutting and Partitioning a Graph aifter a Fixed Pattern (Extended Abstract)
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Multiway cuts in node weighted graphs
Journal of Algorithms
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width
Journal of Algorithms
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
A characterisation of the minimal triangulations of permutation graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Treewidth and minimum fill-in on permutation graphs in linear time
Theoretical Computer Science
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
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Given an undirected graph and pairs of terminals the Restricted Vertex Multicut problem asks for a minimum set of nonterminal vertices whose removal disconnects each pair of terminals. The problem is known to be NP-complete for trees and polynomial-time solvable for interval graphs. In this paper we give a polynomial-time algorithm for the problem on permutation graphs. Furthermore we show that the problem remains NP-complete on split graphs whereas it becomes polynomial-time solvable for the class of co-bipartite graphs.