scholarly journals Algorithms for the rainbow vertex coloring problem on graph classes

2021 ◽  
Author(s):  
Paloma T. Lima ◽  
Erik Jan van Leeuwen ◽  
Marieke van der Wegen
Keyword(s):  
Vertex Coloring ◽  
Coloring Problem ◽  
Graph Classes ◽  
Vertex Coloring Problem

Lower bounds on approximating some variations of vertex coloring problem over restricted graph classes

2020 ◽  
Vol 12 (06) ◽  
pp. 2050086
Author(s):  
Sayani Das ◽  
Sounaka Mishra
Keyword(s):  
Vertex Coloring ◽  
Restricted Class ◽  
Coloring Problem ◽  
Minimization Problems ◽  
Graph Classes ◽  
Color Class ◽  
Vertex Set ◽  
Vertex Coloring Problem ◽  
Text Color ◽  
Dominator Coloring

A [Formula: see text] vertex coloring of a graph [Formula: see text] partitions the vertex set into [Formula: see text] color classes (or independent sets). In minimum vertex coloring problem, the aim is to minimize the number of colors used in a given graph. Here, we consider three variations of vertex coloring problem in which (i) each vertex in [Formula: see text] dominates a color class, (ii) each color class is dominated by a vertex and (iii) each vertex is dominating a color class and each color class is dominated by a vertex. These minimization problems are known as Min-Dominator-Coloring, Min-CD-Coloring and Min-Domination-Coloring, respectively. In this paper, we present approximation hardness results for these problems for some restricted class of graphs.

A DNA computer model for solving vertex coloring problem

2006 ◽  
Vol 51 (20) ◽  
pp. 2541-2549 ◽  
Author(s):  
Jin Xu ◽  
Xiaoli Qiang ◽  
Fang Gang ◽  
Kang Zhou
Keyword(s):  
Computer Model ◽  
Vertex Coloring ◽  
Coloring Problem ◽  
Vertex Coloring Problem ◽  
Dna Computer

A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity

2021 ◽  
pp. 1-11
Author(s):  
Zhaocai Wang ◽  
Dangwei Wang ◽  
Xiaoguang Bao ◽  
Tunhua Wu
Keyword(s):  
Time Complexity ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Vertex Coloring ◽  
Intelligent Computing ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Computing Algorithm ◽  
Vertex Coloring Problem ◽  
Dna Algorithm

The vertex coloring problem is a well-known combinatorial problem that requires each vertex to be assigned a corresponding color so that the colors on adjacent vertices are different, and the total number of colors used is minimized. It is a famous NP-hard problem in graph theory. As of now, there is no effective algorithm to solve it. As a kind of intelligent computing algorithm, DNA computing has the advantages of high parallelism and high storage density, so it is widely used in solving classical combinatorial optimization problems. In this paper, we propose a new DNA algorithm that uses DNA molecular operations to solve the vertex coloring problem. For a simple n-vertex graph and k different kinds of color, we appropriately use DNA strands to indicate edges and vertices. Through basic biochemical reaction operations, the solution to the problem is obtained in the O (kn2) time complexity. Our proposed DNA algorithm is a new attempt and application for solving Nondeterministic Polynomial (NP) problem, and it provides clear evidence for the ability of DNA calculations to perform such difficult computational problems in the future.

The Distance Polytope for the Vertex Coloring Problem

2018 ◽  
pp. 144-156
Author(s):  
Bruno Dias ◽  
Rosiane de Freitas ◽  
Nelson Maculan ◽  
Javier Marenco
Keyword(s):  
Vertex Coloring ◽  
Coloring Problem ◽  
Vertex Coloring Problem

scholarly journals A DNA Computing Model for the Graph Vertex Coloring Problem Based on a Probe Graph

Engineering ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Jin Xu ◽  
Xiaoli Qiang ◽  
Kai Zhang ◽  
Cheng Zhang ◽  
Jing Yang
Keyword(s):  
Dna Computing ◽  
Vertex Coloring ◽  
Graph Vertex ◽  
Coloring Problem ◽  
Computing Model ◽  
Vertex Coloring Problem
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