# Vertex-Coloring with Defects

@article{Angelini2017VertexColoringWD, title={Vertex-Coloring with Defects}, author={Patrizio Angelini and Michael A. Bekos and Felice De Luca and Walter Didimo and Michael Kaufmann and Stephen G. Kobourov and Fabrizio Montecchiani and Chrysanthi N. Raftopoulou and Vincenzo Roselli and Antonios Symvonis}, journal={J. Graph Algorithms Appl.}, year={2017}, volume={21}, pages={313-340} }

Defective coloring is a variant of the traditional vertex-coloring in which adjacent vertices are allowed to have the same color, as long as the induced monochromatic components have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, diameter, and acyclicity of the monochromatic components. We focus on defective colorings with κ colors in which the…

## 13 Citations

Bipartizing with a Matching

- MathematicsCOCOA
- 2018

This work studies the problem of determining whether a given graph G admits a matching M whose removal destroys all odd cycles of G and shows that this problem is fixed-parameter tractable when parameterized by the clique-width, which implies that it is polynomial-time solvable for many interesting graph classes, such as distance-hereditary, outerplanar, and chordal graphs.

Parameterized (Approximate) Defective Coloring

- Mathematics, Computer ScienceSTACS
- 2018

The complexity of Defective Coloring is investigated, and an ETH-based lower bound for treewidth and pathwidth is given, showing that no algorithm can solve the problem in $n^{o(pw)}$, essentially matching the complexity of an algorithm obtained with standard techniques.

Defective and Clustered Graph Colouring

- Mathematics
- 2018

Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic…

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

- Mathematics, Computer ScienceMathematics
- 2020

The asymptotic analysis of some well-known and recent evolutionary operators for finding the chromatic number of a graph G and the necessary and sufficient conditions for the global convergence of evolutionary algorithms are focused on.

On the computational complexity of the bipartizing matching problem

- Mathematics
- 2017

The problem of determining whether a given graph~G=(V,E) admits a matching~$M$ whose removal destroys all odd cycles of~$G$ is studied, and it is shown that the problem is fixed parameter tractable when parameterized by the clique-width, which implies polynomial-time solution for many interesting graph classes, such as distance-hereditary, outerplanar, and chordal graphs.

A New Multi-Objective Evolutionary Approach to Graph Coloring and Channel Allocation Problems

- Computer ScienceJournal of Applied Mathematics and Computation
- 2021

A new multi-objective evolutionary algorithm using the new evolutionary operators with multi- objectives in finding the solution to graph coloring and channel allocation and achieves better solution compared to some of the existing well known methods.

Solution to Graph Coloring Using Genetic and Tabu Search Procedures

- Mathematics
- 2018

Some of the engineering applications warrant the solution of Graph Coloring Problem, an NP-hard combinatorial optimization problem. This paper focuses on designing three new evolutionary operators…

Graph Coloring In Optimization Total Waste Transport Vehicles In Bandung

- Business
- 2020

Waste is a material that is produced from human activities that are no longer used and disposed of. Waste management really needs support and commitment from the government to produce sustainable…

Sobre (2,1)-colorações em grafos exoplanares maximais

- Anais do VI Encontro de Teoria da Computação (ETC 2021)
- 2021

Uma $(m, d)$-coloração $\pi$ de um grafo $G$ é uma atribuição de $m$ cores aos vértices do grafo de maneira que, para todo vértice $u$ de $G$, no máximo $d$ vizinhos de $u$ possuem a cor $\pi(u)$.…

Solving Graph Coloring Problem Using Divide and Conquer-Based Turbulent Particle Swarm Optimization

- Computer ScienceArabian Journal for Science and Engineering
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