Now showing items 1-9 of 9

• #### B-chromatic number: Beyond NP-hardness ﻿

(Conference object; Peer reviewed; Journal article, 2015)
The b-chromatic number of a graph G, chi_b(G), is the largest integer k such that G has a k-vertex coloring with the property that each color class has a vertex which is adjacent to at least one vertex in each of the other ...
• #### Complexity of the Steiner Network Problem with Respect to the Number of Terminals ﻿

(Journal article; Peer reviewed, 2019)
In the Directed Steiner Network problem we are given an arc-weighted digraph G, a set of terminals T subseteq V(G) with |T|=q, and an (unweighted) directed request graph R with V(R)=T. Our task is to output a subgraph H ...
• #### Decomposition of map graphs with applications ﻿

(Peer reviewed; Journal article, 2019)
• #### Finding even subgraphs even faster ﻿

(Conference object; Peer reviewed; Journal article, 2015)
Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on n vertices and a positive integer parameter k, find if there exist k ...
• #### Going Far From Degeneracy ﻿

(Peer reviewed; Journal article, 2019-09-06)
An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least ...
• #### Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree ﻿

(Peer reviewed; Journal article, 2019)
In the Steiner Tree problem, we are given as input a connected $n$-vertex graph with edge weights in $\{1,2,\ldots,W\}$, and a set of $k$ terminal vertices. Our task is to compute a minimum-weight tree that contains ...
• #### Quick but odd growth of cacti ﻿

(Conference object; Peer reviewed; Journal article, 2015)
Let F be a family of graphs. Given an input graph G and a positive integer k, testing whether G has a k-sized subset of vertices S, such that G\S belongs to F, is a prototype vertex deletion problem. These type of problems ...
• #### Rank vertex cover as a natural problem for algebraic compression ﻿

(Journal article; Peer reviewed, 2019)
The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem was a long-standing, notorious open problem in parameterized complexity. Some years ago, the breakthrough work by Kratsch and ...
• #### Refined Complexity of PCA with Outliers ﻿

(Conference object; Peer reviewed; Journal article, 2019)
Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and ...