m-Secure vertex cover of a graph

2018 ◽  
Vol 10 (06) ◽  
pp. 1850075
Author(s):  
P. Roushini Leely Pushpam ◽  
Chitra Suseendran
Keyword(s):  
Vertex Cover ◽  
Covering Number ◽  
The Other ◽  
Vertex Cover Problem ◽  
Vertex Covering ◽  
Before And After ◽  
Minimum Number ◽  
Cover Problem

In this paper, we use multiple guard movements to defend the edges of a graph [Formula: see text] against a single attack. At most, one guard is positioned at each vertex. To defend an attack on an edge, a guard at an incident vertex moves across the attacked edge and the other guards may move (or not) to the neighboring vertices to better configure themselves. This strategy requires the set of vertices containing guards to be a vertex cover before and after an attack. A suitable placement of guards is called an [Formula: see text]-secure vertex cover of [Formula: see text]. We call this the [Formula: see text]-secure vertex cover problem, where [Formula: see text] stands for the multiple guard movements. The minimum number of guards required to defend the edges of [Formula: see text] against a single attack using multiple guard movements is called the [Formula: see text]-secure vertex covering number and it is denoted by [Formula: see text]. In this paper we initiate a study of this parameter.

scholarly journals Coloring and Guarding Arrangements

2013 ◽  
Vol Vol. 15 no. 3 (Combinatorics) ◽  
Author(s):  
Prosenjit Bose ◽  
Jean Cardinal ◽  
Sébastien Collette ◽  
Ferran Hurtado ◽  
Matias Korman ◽  
...  
Keyword(s):  
Chromatic Number ◽  
Vertex Cover ◽  
Minimum Size ◽  
Vertex Cover Problem ◽  
Minimum Number ◽  
International Audience ◽  
A Cell ◽  
Cover Problem ◽  
Minimum Vertex Cover Problem ◽  
Arrangement Of Lines

Combinatorics International audience Given an arrangement of lines in the plane, what is the minimum number c of colors required to color the lines so that no cell of the arrangement is monochromatic? In this paper we give bounds on the number c both for the above question, as well as some of its variations. We redefine these problems as geometric hypergraph coloring problems. If we define $\Hlinecell$ as the hypergraph where vertices are lines and edges represent cells of the arrangement, the answer to the above question is equal to the chromatic number of this hypergraph. We prove that this chromatic number is between Ω(logn/loglogn). and O(n√). Similarly, we give bounds on the minimum size of a subset S of the intersections of the lines in A such that every cell is bounded by at least one of the vertices in S. This may be seen as a problem on guarding cells with vertices when the lines act as obstacles. The problem can also be defined as the minimum vertex cover problem in the hypergraph $\Hvertexcell$, the vertices of which are the line intersections, and the hyperedges are vertices of a cell. Analogously, we consider the problem of touching the lines with a minimum subset of the cells of the arrangement, which we identify as the minimum vertex cover problem in the $\Hcellzone$ hypergraph.

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

Quantum Algorithms of the Vertex Cover Problem on a Quantum Computer

2009 ◽  
Author(s):  
Weng-Long Chang ◽  
Ting-Ting Ren ◽  
Mang Feng ◽  
Shu-Chien Huang ◽  
Lai Chin Lu ◽  
...  
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem

scholarly journals On the max min vertex cover problem

2015 ◽  
Vol 196 ◽  
pp. 62-71 ◽  
Author(s):  
Nicolas Boria ◽  
Federico Della Croce ◽  
Vangelis Th. Paschos
Keyword(s):  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem
Sign in / Sign up

Export Citation Format

Share Document