Item description for Graph Colouring and the Probabilistic Method by Michael S. O. Molloy & Bruce A. Reed...
Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality. The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta) colouring; algorithmic variants of the Local Lemma which permit the efficient construction of many optimal and near-optimal colourings. This begins with a gentle introduction to the probabilistic method and will be useful to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability.
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Est. Packaging Dimensions: Length: 1" Width: 6.25" Height: 9.25" Weight: 1.4 lbs.
Release Date Dec 6, 2001
ISBN 3540421394 ISBN13 9783540421399
Availability 0 units.
More About Michael S. O. Molloy & Bruce A. Reed
Appreciation for religion was programmed into me when I was young--before I had any chance to resist its fascination. My grandmothers were my first teachers. When my mother's mother was 19 she went to Paris to study painting and to experience cultural life there. She stayed in Paris for two years, and it was a turning point in her life. She returned home to create paintings, which surrounded me as I grew up in Los Angeles. She also returned with hundreds of photographs of religious statues, paintings, and other objects, as well as a thirst to take her grandchildren to museums and churches. My other grandmother was a choir director, and I remember many hours spent in the choir loft, which vibrated from the pedal notes of the organ music. It was through art and music that I discovered the richness of religion. Early experiences like these led me to leave the country after college in order to see the world, and my travels made me recognize how much people and their cultures are shaped by religions. When I returned, I studied religion formally. My MA degree (at St. John's University) allowed me to study the images of darkness in Jewish and Christian mystical literature. I received a scholarship from the East-West Center in Hawaii, and in Hawaii my life began to be influenced by the thought of Asia. For my Ph.D. (at the University of Hawaii) I wrote on the Hindu and Buddhist mysticism to be found in the writings of Aldous Huxley. I had the pleasure of meeting Huxley's wife Laura in Los Angeles, interviewing people who knew him, and reading his original manuscripts at UCLA. I did graduate work at Banaras Hindu University, and later studied traditional Japanese arts--including kendo, teaceremony, ceramics, and calligraphy--in Kyoto. I have practiced meditation at Christian and Buddhist monasteries in Asia, Europe, and the United States. I am currently writing a book for McGraw-Hill on Christianity. I live in Honolulu.
Reviews - What do customers think about Graph Colouring and the Probabilistic Method?
Good for every graph theorist Mar 8, 2002
This is definitely for someone who knows graph theory very well and 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 this book is a good source.