Markus S. Dregi

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We give an algorithm that for an input n-vertex graph G and integer k &gt; 0, in time O(c<sup>k</sup>n) either outputs that the tree width of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for tree width which runs in time single-exponential in k and(More)
We give an algorithm that for an input n-vertex graph G and integer k > 0, in time O(cn) either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single-exponential in k and linear in n. Treewidth(More)
We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-hard, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics,(More)
We prove that for every positive integer r and for every graph class G of bounded expansion, the r-Dominating Set problem admits a linear kernel on graphs from G. Moreover, when G is only assumed to be nowhere dense, then we give an almost linear kernel on G for the classic Dominating Set problem, i.e., for the case r = 1. These results generalize a line of(More)
The Weighted Vertex Integrity (wVI) problem takes as input an n-vertex graph G, a weight function $$w:V(G)\rightarrow {\mathbb {N}}$$ w : V ( G ) → N , and an integer p. The task is to decide if there exists a set $$X\subseteq V(G)$$ X ⊆ V ( G ) such that the weight of X plus the weight of a heaviest component of $$G-X$$ G - X is at most p. Among other(More)
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