Guide to Graph Colouring: Algorithms and Applications

@article{Lewis2021GuideTG,
  title={Guide to Graph Colouring: Algorithms and Applications},
  author={R. M. R. Lewis},
  journal={Guide to Graph Colouring},
  year={2021}
}
  • R. Lewis
  • Published 27 October 2015
  • Computer Science
  • Guide to Graph Colouring
This book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain… 
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70 Citations
Highly Influential Citations
4
Background Citations
28
Methods Citations
12
Results Citations
3

70 Citations

Citation Type

Citation Type

Graph coloring: a novel heuristic based on trailing path—properties, perspective and applications in structured networks
TLDR
A novel heuristic is presented, namely the ‘trailing path’, which returns an approximate solution of the chromatic number within P time, and with a better accuracy than most existing algorithms.
Tackling the edge dynamic graph colouring problem with and without future adjacency information
TLDR
This paper presents several heuristic methods for modifying a feasible colouring at time-step t into an initial, but not necessarily feasible, colouring for a “similar” graph atTime-step $$t+1$$t-1+1.
An Exact Cutting Plane Algorithm to Solve the Selective Graph Coloring Problem in Perfect Graphs
GRAPH COLORING FOR EFFICIENT COURSE AND EXAM SCHEDULING USING MATLAB
TLDR
This work has designed and developed a scheduling application which receives as input courses and constraints and outputs an efficient lecture/examination schedule and a more involved coloring algorithm for addressing more complex course scheduling instances while minimizing required time resources.
The maximum happy induced subgraph problem: Bounds and algorithms
An Incremental SAT-Based Approach to the Graph Colouring Problem
TLDR
A CEGAR-based (Counter-Example Guided Abstraction Refinement) approach that only encodes a part of the problem and then adds the missing constraints in an incremental way until a valid solution with k colours is found or the unsatisfiable problem is proven, meaning that the chromatic number of the graph is greater than k.
Tackling the maximum happy vertices problem in large networks
TLDR
This paper designs and test a tabu search approach and proposes an algorithm for imposing additional precoloured vertices and is able to significantly reduce the solution space of the maximum happy vertices problem.
Recycling Solutions for Vertex Coloring Heuristics
TLDR
This work proposes a simple initial solution generator, the recycle method, which makes use of the legal (k+1)-coloring that has been found and is expected to guide a general heuristic algorithm to find a legal k-coloring quickly, as demonstrated by experimental studies.
Exact Algorithms for Weighted Coloring in Special Classes of Tree and Cactus Graphs
TLDR
This work improves the exact algorithms for solving WV CP on binary trees and proposes new and efficient algorithms for WVCP on cycles and cactus paths with maximum degree three.
High-Performance Parallel Graph Coloring with Strong Guarantees on Work, Depth, and Quality
TLDR
The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and to color vertices in the order dictated by this relaxation, which introduces a tunable amount of parallelism into the degeneracy ordering that is otherwise hard to parallelize.
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