On the complexity of testing for odd holes and induced odd paths
Discrete Mathematics
Induced circuits in planar graphs
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
On the efficiency of polynomial time approximation schemes
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Information Processing Letters
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
A Polynomial Algorithm for Recognizing Perfect Graphs
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The turing way to parameterized complexity
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Hole and antihole detection in graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized Complexity
Multiple Hypernode Hitting Sets and Smallest Two-Cores with Targets
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Complexity results related to monophonic convexity
Discrete Applied Mathematics
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Consider the following problem, which we call "Chordless path through three vertices" or Cp3v, for short: Given a simple undirected graph G = (V, E), a positive integer k, and three distinct vertices s, t, and v ∈ V, is there a chordless path of length at most k from s via v to t in G? In a chordless path, no two vertices are connected by an edge that is not in the path. Alternatively, one could say that the subgraph induced by the vertex set of the path in G is the path itself. The problem has arisen in the context of service deployment in communication networks. We resolve the parametric complexity of Cp3v by proving it W[1]-complete with respect to its natural parameter k. Our reduction extends to a number of related problems about chordless paths and cycles. In particular, deciding on the existence of a single directed chordless (s, t)-path in a digraph is also W[1]-complete with respect to the length of the path.