Parameterized Complexity of Generalized Vertex Cover Problems

2005 ◽  
pp. 36-48 ◽  
Author(s):  
Jiong Guo ◽  
Rolf Niedermeier ◽  
Sebastian Wernicke
Keyword(s):  
Parameterized Complexity ◽  
Vertex Cover

scholarly journals On the parameterized complexity of vertex cover and edge cover with connectivity constraints

2015 ◽  
Vol 565 ◽  
pp. 1-15 ◽  
Author(s):  
Henning Fernau ◽  
Fedor V. Fomin ◽  
Geevarghese Philip ◽  
Saket Saurabh
Keyword(s):  
Parameterized Complexity ◽  
Vertex Cover ◽  
Edge Cover

scholarly journals A Parameterized Complexity View on Collapsing k-Cores

2021 ◽  
Author(s):  
Junjie Luo ◽  
Hendrik Molter ◽  
Ondřej Suchý
Keyword(s):  
Parameterized Complexity ◽  
Undirected Graph ◽  
Minimum Degree ◽  
Structural Parameters ◽  
Vertex Cover ◽  
Polynomial Kernel ◽  
Input Graph ◽  
Induced Subgraph ◽  
Vertex Deletion ◽  
Drop Outs

AbstractWe study the -hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced subgraph with minimum degree k, has size at most x. Collapsed k-Core was introduced by Zhang et al. (2017) and it is motivated by the study of engagement behavior of users in a social network and measuring the resilience of a network against user drop outs. Collapsed k-Core is a generalization of r-Degenerate Vertex Deletion (which is known to be -hard for all r ≥ 0) where, given an undirected graph G and integers b and r, we are asked to remove b vertices such that the remaining graph is r-degenerate, that is, every its subgraph has minimum degree at most r. We investigate the parameterized complexity of Collapsed k-Core with respect to the parameters b, x, and k, and several structural parameters of the input graph. We reveal a dichotomy in the computational complexity of Collapsed k-Core for k ≤ 2 and k ≥ 3. For the latter case it is known that for all x ≥ 0 Collapsed k-Core is -hard when parameterized by b. For k ≤ 2 we show that Collapsed k-Core is -hard when parameterized by b and in when parameterized by (b + x). Furthermore, we outline that Collapsed k-Core is in when parameterized by the treewidth of the input graph and presumably does not admit a polynomial kernel when parameterized by the vertex cover number of the input graph.

Parameterized Complexity of Vertex Cover Variants

2007 ◽  
Vol 41 (3) ◽  
pp. 501-520 ◽  
Author(s):  
Jiong Guo ◽  
Rolf Niedermeier ◽  
Sebastian Wernicke
Keyword(s):  
Parameterized Complexity ◽  
Vertex Cover

scholarly journals Parameterized complexity of coloring problems: Treewidth versus vertex cover

2011 ◽  
Vol 412 (23) ◽  
pp. 2513-2523 ◽  
Author(s):  
Jiří Fiala ◽  
Petr A. Golovach ◽  
Jan Kratochvíl
Keyword(s):  
Parameterized Complexity ◽  
Vertex Cover

Complexity of the Maximum k-Path Vertex Cover Problem

2020 ◽  
Vol E103.A (10) ◽  
pp. 1193-1201
Author(s):  
Eiji MIYANO ◽  
Toshiki SAITOH ◽  
Ryuhei UEHARA ◽  
Tsuyoshi YAGITA ◽  
Tom C. van der ZANDEN
Keyword(s):  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem

scholarly journals Approximation algorithm for minimum connected 3-path vertex cover

2020 ◽  
Vol 287 ◽  
pp. 77-84
Author(s):  
Pengcheng Liu ◽  
Zhao Zhang ◽  
Xianyue Li ◽  
Weili Wu
Keyword(s):  
Approximation Algorithm ◽  
Vertex Cover
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