We present an algorithm with runtime $O(k^{2k}n^3m) for the k-Interval Completion problem of deciding whether a graph on n vertices and m edges can be made into an interval graph by adding at most k edges.Expand

The {\sc $k$-Leaf Out-Branching} problem is to find an out-branching, that is a rooted oriented spanning tree, with at least $k leaves in a given digraph.Expand

We give an algorithm solving this optimization problem on any $n$-vertex graph $G$ in time ${\cal O}(|\Pi_G| \cdot n^{t+4}\cdot f(t,\varphi))$, where $\varphi$ is a counting monadic second order logic formula and $t\geq 0$ be an integer.Expand

We present an algorithm with runtime O(k(2k)n3 * m) for the following NP-complete problem: Given an arbitrary graph G on n vertices and m edges, can we obtain an interval graph by adding at most kâ€¦ Expand

We show that given an n-vertex graph G together with its set of potential maximal cliques, and an integer t, it is possible in time the number of potential minimal cliques times $O(n^{O(t)})$ to find a maximum induced subgraph of treewidth t in G.Expand