Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques
Theory of Computing Systems
Open problems around exact algorithms
Discrete Applied Mathematics
On the number of maximal bipartite subgraphs of a graph
Journal of Graph Theory
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
Treewidth Computation and Extremal Combinatorics
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
On Independent Sets and Bicliques in Graphs
Graph-Theoretic Concepts in Computer Science
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Fixed-parameter tractability results for feedback set problems in tournaments
Journal of Discrete Algorithms
Set Partitioning via Inclusion-Exclusion
SIAM Journal on Computing
Iterative compression and exact algorithms
Theoretical Computer Science
Feedback vertex sets in tournaments
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Fast exponential algorithms for maximum γ-regular induced subgraph problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Finding odd cycle transversals
Operations Research Letters
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
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We study combinatorial and algorithmic questions around minimal feedback vertex sets (FVS) in tournament graphs. On the combinatorial side, we derive upper and lower bounds on the maximum number of minimal FVSs in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740n minimal FVSs, and that there is an infinite family of tournaments, all having at least 1.5448n minimal FVSs. This improves and extends the bounds of Moon (1971). On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal FVSs of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum-sized FVS in a tournament. © 2013 Wiley Periodicals, Inc. (Part of this research has been supported by the Netherlands Organisation for Scientific Research (NWO), grant 639.033.403. A preliminary version of this article appeared in the Proceedings of ESA 2010.)