© 2016

A Guide to Graph Colouring

Algorithms and Applications


Table of contents

  1. Front Matter
    Pages i-xiv
  2. R. M. R. Lewis
    Pages 1-25
  3. R. M. R. Lewis
    Pages 27-54
  4. R. M. R. Lewis
    Pages 55-77
  5. R. M. R. Lewis
    Pages 79-109
  6. R. M. R. Lewis
    Pages 111-149
  7. R. M. R. Lewis
    Pages 151-167
  8. R. M. R. Lewis
    Pages 169-193
  9. R. M. R. Lewis
    Pages 195-221
  10. Back Matter
    Pages 223-253

About this book


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 graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code.


The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.


Combinatorial Optimization Graph Theory Heuristics Metaheuristics Operations Research Optimization Scheduling

Authors and affiliations

  1. 1.Cardiff School of MathematicsCardiff UniversityCardiffUnited Kingdom

About the authors

Dr. Rhyd Lewis is a lecturer in operational research at Cardiff School of Mathematics, Cardiff University. Previously he was a lecturer in quantitative methods at Cardiff Business School. He holds a Ph.D. in Computer Science and Operational Research from Edinburgh Napier University. His research interests cover the analysis and application of metaheuristic algorithms, with particular focus on timetabling, graph colouring, and bin packing, vehicle routing, arc routing, and grouping/partitioning problems, and he has been a program committee member for the key related conferences, such as EvoCop, GECCO, MIC, and PATAT, and he is a cofounder and associate editor of the Intl. J. of Metaheuristics.

Bibliographic information

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“The book gives a comprehensive description and handling on arguably one of the most important notions of combinatorics—graph coloring. … The book is nicely written, and carries a big pile of information valuable for both users and researchers in the field.” (András Sándor Pluhár, Mathematical Reviews, February, 2017)

“This well-written book will serve as a utilitarian guide to graph coloring and its practical applications. It includes many definitions, theorems, proofs, algorithms, and pointers for further reading. The book will be helpful for teaching courses on graph coloring to students of mathematics and computer science. I strongly recommend it for the intended audience.” (S. V. Nagaraj, Computing Reviews,, June, 2016)

“The book is a comprehensive guide to graph colouring algorithms. … The book is a nice textbook for both undergraduate and graduate students in the areas of operations research and theoretical computer science. … Finally, it is a good source of knowledge for practitioners.” (Marcin Anholcer, zbMATH 1330.05002, 2016)