Remarks on Hamiltonian properties of powers of digraphs
2nd Twente workshop on Graphs and combinatorial optimization
P-Complete Approximation Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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In this paper we study the complexity of finding a spanning cactus in various graphs. First, we show that the task of determining if there is a directed spanning cactus in a general unweighted digraph is NP-complete. The proof is a reduction from ONE-IN-THREE 3SAT. Secondly, we show that finding the minimum spanning cactus in a directed, weighted complete graph with triangle inequality is polynomial time equivalent to finding the minimum travelling salesman problem (TSP) tour in the same graph and that they have the same hardness in approximation.