Handbook of combinatorics

Author(s)

• Graham, Ronald L.
• Grötschel, Martin
• Lovász, László

Bibliographic Information

Handbook of combinatorics

edited by R.L. Graham, M. Grötschel, L. Lovász

Elsevier , MIT Press, 1995

• : set : Elsevier
• : set : MIT Press
• v. 1 : Elsevier
• v. 1 : MIT
• v. 2 : Elsevier
• v. 2 : MIT

Note

"North-Holland"--Cover of v. 1

Includes bibliographical references and indexes in each vol

Description and Table of Contents

Volume

: set : MIT Press ISBN 9780262571722

Description

Combinatorics, the branch of mathematics that deals with the study of discrete, usually finite, structures, covers a wide range of problems not only in mathematics but also in the biological sciences, engineering, and computer science. Handbook of Combinatorics covers almost every aspect of this enormous field, including combinatorics in graph theory, theoretical computer science, optimization, and convexity theory and applications in operations research, electrical engineering, statistical mechanics, chemistry, molecular biology, pure mathematics, and computer science.

Volume

v. 1 : Elsevier ISBN 9780444823465

Description

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.

Table of Contents

Part I: Structures.Graphs. Basic graph theory: paths and circuits (J.A. Bondy). Connectivity and network flows (A. Frank). Matchings and extensions (W.R. Pulleyblank). Colouring, stable sets, and perfect graphs (B. Toft). Embeddings and minors (C. Thomassen). Random graphs (M. Karo ski). Finite Sets and Relations. Hypergraphs (P. Duchet). Partially ordered sets (W.T. Trotter). Matroids. Matroids: fundamental concepts (D.J.A. Welsh). Matroid minors (P.D. Seymour). Matroid optimization and algorithms (R.E. Bixby, W.H. Cunningham). Symmetric Structures. Permutation groups (P.J. Cameron). Finite geometries (P.J. Cameron). Block designs (A.E. Brouwer). Association schemes (A.E. Brouwer, W. Haemers). Codes (J.H. van Lint). Combinatorial Structures in Geometry and Number Theory. Extremal problems in combinatorial geometry (P. Erdoes, G. Purdy). Convex polytopes and related complexes (V. Klee, P. Kleinschmidt). Point lattices (J.C. Lagarias). Combinatorial number theory (C. Pomerance, A. Sarkoezy). Author Index. Subject Index.

Volume

v. 2 : Elsevier ISBN 9780444823519

Description

Covering important results and current trends and issues across the spectrum of combinatorics, this volume covers extremal graph theory, optimization, polyhedral combinatorics, combinatorics in electrical engineering and other related topics.

Table of Contents

Part II: Aspects. Algebraic enumeration (I.M. Gessel, R.P. Stanley). Asymptotic enumeration methods (A.M. Odlyzko). Extremal graph theory (B. Bollobas). Extremal set systems (P. Frankl). Ramsey Theory (J. Neset il). Discrepancy theory (J. Beck, V.T. Sos). Automorphism groups, isomorphism, reconstruction (L. Babai). Optimization (M. Groetschel, L. Lovasz). Computational complexity (D.B. Shmoys, E. Tardos).Part III: Methods. Polyhedral combinatorics (A. Schrijver). Tools from linear algebra (C.D. Godsil). Tools from higher algebra (N. Alon). Probabilistic methods (J. Spencer). Topological methods (A. Bjoerner).Part IV: Applications. Combinatorics in operations research (A. Kolen, J.K. Lenstra). Combinatorics in electrical engineering and statics (A. Recski). Combinatorics in statistical mechanics (C.D. Godsil, M. Groetschel, D.J.A. Welsh). Combinatorics in chemistry (D.H. Rouvray). Applications of combinatorics to molecular biology (M.S. Waterman). Combinatorics in computer science (L. Lovasz, D.B. Shmoys, E. Tardos). Combinatorics in pure mathematics (L. Lovasz, L. Pyber, D.J.A. Welsh, G.M. Ziegler).Part V: Horizons. Infinite combinatorics (A. Hajnal). Combinatorial games (R.K. Guy). The history of combinatorics (N.L. Biggs, E.K. Lloyd, R.J. Wilson). Author Index. Subject Index.

Volume

: set : Elsevier ISBN 9780444880024

Description

One area of mathematics which has come to the fore in recent years is that of combinatorics. The intense interest has been fuelled in large part by the increasing importance of computers, the needs of computer science and the demands from applications where discrete models play more and more important roles. In addition, many classical branches of mathematics have now come to recognize that combinatorial structures are essential components of many mathematical theories. Leading experts in all areas of combinatorics have contributed to this book. The "Handbook of Combinatorics" provides the working mathematician and computer scientist with an overview of basic methods and paradigms. The book also covers important results and discusses current trends and issues across the whole spectrum of combinatorics. It is hoped that even specialists in the field will benefit from reading this handbook by learning a leading expert's coherent and individual view of the topic.

Table of Contents

• Part 1 Structures: graphs - basic graph theory - paths and circuits, J.A. Bondy, connectivity and network flows, A. Frank, matchings and extensions, W.R. Pulleyblank, colouring, stable sets and perfect graphs, B. Toft, embeddings and minors, C. Thomassen, random graphs, M. Karonski
• finite sets and relations - hypergraphs, P. Duchet, partially ordered sets, W.T. Trotter
• matroids - matroids - fundamental concepts, D.J.A. Welsh, matroid minors, P.D. Seymour, matroid optimization and algorithms, R.E. Bixby and W.H. Cunningham
• symmetric structures - permutation groups, P.J. Cameron, finite geometries, P.J. Cameron, block designs, A.E. Brouwer, association schemes, A.E. Brouwer and W. Haemers, codes, J.H. van Lint
• combinatorial structures in geometry and number theory - extremal problems in combinatorial geometry, P. Erdos and G. Purdy, convex polytopes and related complexes, V. Klee and P. Kleinschmidt, point lattices, J.C. Lagarias, combinatorial number theory, C. Pomerance and A. Sarkozy. Part 2 Aspects: algebraic enumeration, I.M. Gessel and R.P. Stanley
• asymptotic enumeration methods, A.M. Odlyzko
• extremal graph theory, B. Bollobas
• extremal set systems, P. Frankl
• Ramsey theory, J. Nesetril
• discrepancy theory, J. Beck and V.T. Sos
• automorphism groups, isomorphism, reconstruction, L. Babai
• optimization, M. Grotschel and L. Lovasz
• computational complexity, D.B. Shmoys and E. Tardos. Part 3 Methods: polyhedral combinatorics, A. Schrijver
• tools from linear algebra, C.D. Godsil
• tools from higher algebra, N. Alon
• probabilistic methods, J. Spencer
• topological methods, A. Bjorner. Part 4 Applications: combinatorics in operations research, A. Kolen and J.K. Lenstra
• combinatorics in electrical engineering and statics, A. Recski
• combinatorics in statistical mechanics, C.D. Godsil et al
• combinatorics in chemistry, D.H. Rouvray
• applications of combinatorics to molecular biology, M.S. Waterman
• combinatorics in computer science, L. Lovasz et al
• combinatorics in pure mathematics, L. Lovasz et al. Part 5 Horizons: infinite combinatorics, A. Hajnal
• combinatorial games, R.K. Guy
• the history of combinatorics, N.L. Biggs et al.

by "Nielsen BookData"

Details

• NCID: BA26623705
• ISBN:
  • 044488002X
  • 0262571722
  • 0444823468
  • 0262571706
  • 0444823514
  • 0262571714
• LCCN: 95022116
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Amsterdam ; Tokyo,Cambridge, Mass.
• Pages/Volumes: 2 v. (xii, 2198 p.)
• Size: 25 cm
• Classification:
  • LCC : QA164
  • DC20 : 511/.6
• Subject Headings:
  • LCSH : Combinatorial analysis -- Handbooks, manuals, etc