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• #### Computing minimal triangulation in Time o(n^2.376) ﻿

(Journal article, 2005)
• #### Exact algorithms for treewidth and minimum fill-in ﻿

(Journal article, 2006)
• #### Exploring Subexponential Parameterized Complexity of Completion Problems ﻿

(Peer reviewed; Journal article, 2014-02-19)
Let F be a family of graphs. In the F-Completion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k edges can be added to G so that the resulting graph does not contain a graph ...
• #### Finding Induced Subgraphs via Minimal Triangulations ﻿

(Conference object; Peer reviewed; Journal article, 2010)
Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulation problems in- cluding Minimum Fill-in and Treewidth. We discover unexpected ...
• #### Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves ﻿

(Conference object; Peer reviewed; Journal article, 2009)
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. The problem has recently received much attention from the ...
• #### Largest chordal and interval subgraphs faster than 2n ﻿

(Peer reviewed; Journal article, 2015-08-22)
We prove that in a graph with n vertices, induced chordal and interval subgraphs with the maximum number of vertices can be found in time O(2λn) for some λ< 1. These are the first algorithms breaking the trivial 2nnO(1) ...
• #### Lex M versus MCS-M ﻿

(Journal article, 2006)
• #### Minimum Fill-in of Sparse Graphs: Kernelization and Approximation ﻿

(Conference object; Peer reviewed; Journal article, 2011)
The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop ...
• #### New Results on Minimal Triangulations ﻿

(Doctoral thesis, 2006-04-25)
• #### Tight bounds for parameterized complexity of Cluster Editing ﻿

(Conference object; Peer reviewed; Journal article, 2013)
In the Correlation Clustering problem, also known as Cluster Editing, we are given an undirected graph G and a positive integer k; the task is to decide whether G can be transformed into a cluster graph, i.e., a disjoint ...
• #### A Vertex Incremental Approach for Maintening Chordiality ﻿

(Journal article, 2006)
• #### A wide-range algorithm for minimal triangulation from an arbitrary ordering ﻿

(Journal article, 2006)