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
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
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
Fixed-parameter complexity of feedback vertex set in bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Minimal dominating sets in graph classes: combinatorial bounds and enumeration
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Feedback Vertex Sets in Tournaments
Journal of Graph Theory
An exact algorithm for subset feedback vertex set on chordal graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740n minimal feedback vertex sets and that there is an infinite family of tournaments, all having at least 1.5448n minimal feedback vertex sets. This improves and extends the bounds of Moon (1971). On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal feedback vertex sets of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum size feedback vertex set in a tournament.