Graph Colouring and the Probabilistic Method 2002nd Edition by Michael Molloy (PDF)

Description

Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand’s concentration inequality.

User’s Reviews

Editorial Reviews: Review From the reviews of the first edition:”The presented book contains many … chapters, each of which presents a proof technique and apply that for a certain graph coloring problem. … The book ends with a vast bibliography. We think that this well-written monograph will serve as a main reference on the subject for years to come.” (János Barát, Acta Scientiarum Mathematicarum, Vol. 69, 2003)”The book is a pleasure to read; there is a clear, successful attempt to present the intuition behind the proofs, making even the difficult, recent proofs of important results accessible to potential readers. … The book is highly recommended to researchers and graduate students in graph theory, combinatorics, and theoretical computer science who wish to have this ability.” (Noga Alon, SIAM Review, Vol. 45 (2), 2003)”The probabilistic method in graph theory was initiated by Paul Erdös in 1947 … . This book is an introduction to this powerful method. … The book is well-written and brings the researcher to the frontiers of an exciting field.” (M.R. Murty, Short Book Reviews, Vol. 23 (1), April, 2003)”This monograph provides an accessible and unified treatment of major advances made in graph colouring via the probabilistic method. … Many exercises and excellent remarks are presented and discussed. Also very useful is the list of up-to-date references for current research. This monograph will be useful both to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability.” (Jozef Fiamcik, Zentralblatt MATH, Vol. 987 (12), 2002)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is definitely for someone who knows graph theory very welland wants to learn the powerful tool of “probabilistic method”.As far as I know, this is the second book on the probabilistic method (the first one is by Alon and Spencer). It starts with some simple basic notions and gradually takes you to the heart of some deep (and complicated) results in graph theory. Although the technique can be used in different areas of combinatorics and theoretical computer science, almost all examples and problems in the book are related to graph theory (and specially graph coloring). One of the good points about this book is that they usually provide good intuitions for the proofs before going into their details.If you consider yourself a combinatorist or a theoretical computer scientist and you don’t know much about this tool thisbook is a good source.

⭐This is a great book for any mathematical library. The print edition is very readable and the examples are helpful. I purchased the kindle version and quickly found several problems with the mathematical typesetting in the book. When I compared the kindle version to the print version formulas were often missing symbols including summations, subtraction signs, and parenthesis. This made many of the equations and expressions unreadable. While most of the typesetting was fine there were enough errors that I chose to return the kindle book for a refund. I informed amazon customer service and they appear to be working on the problem because as of this writing the kindle book is no longer available for purchase.

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