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We provide an algorithm listing all minimal dominating sets of a graph on <i>n</i> vertices in time <i>O</i>(1.7159<sup><i>n</i></sup>). This result can be seen as an algorithmic proof of the fact that the number of minimal dominating sets in a graph on <i>n</i> vertices is at most 1.7159<sup><i>n</i></sup>, thus improving on the trivial… (More)

We present an O(1.7548 n) algorithm finding a minimum feedback vertex set in a graph on n vertices.

We show that the number of minimal dominating sets in a graph on n vertices is at most 1.7697 n , thus improving on the trivial O(2 n / √ n) bound. Our result makes use of the measure and conquer technique from exact algorithms, and can be easily turned into an O(1.7697 n) listing algorithm. Based on this result, we derive an O(2.8805 n) algorithm for the… (More)

We present a time O(1.7548 n) algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638 n minimal feedback vertex sets and that there exist graphs having 105 n/10 ≈ 1.5926 n minimal feedback vertex sets.

- Frederic Dorn, Joanna Bauer, Lene Favrholdt, Serge Gaspers, Petr Golovach, Pinar Heggernes +31 others
- 2007

In this thesis we focus on subexponential algorithms for NP-hard graph problems: exact and parameterized algorithms that have a truly subexponential running time behavior. For input instances of size n we study exact algorithms with running time 2 O(√ n) and parameterized algorithms with running time 2 O(√ k) ·n O(1) with parameter k, respectively. We study… (More)

We present an O(1.7548 n) algorithm finding a minimum feedback vertex set in a graph on n vertices.

A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x = y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. A graph is representable if and only if it is k-representable for some k [1]. In this note, we… (More)