Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics.
The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors.
The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry.
The selection is a valuable reference for researchers interested in combinatorics.
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Ronald L. Graham is Irwin and Joan Jacobs Professor in the Department of Computer Science and Engineering and Chief Scientist of the California Institute for Telecommunications and Information Technology, University of California, San Diego.
László Lovász is Senior Researcher in the Theory Group at Microsoft Research.
"If you need to know about the...applications of discrete structures, you'll probably find whatever you're looking for here."
— IEEE Micro Review
"The Handbook of Combinatorics will be a work of quality and significance in what has become, over the past 20 years, one of the most active and fruitful areas of mathematical research. The editors, who are top people in the field, have collected a distinguished group of authors. The Handbook will be a major and central scholarly work."
—Hartley Rogers, Jr., Professor, Massachusetts Institute of Technology
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