Handbook of Combinatorics, Volume 1

Front Cover
Elsevier, Dec 25, 1995 - Mathematics - 2198 pages
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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Contents

University of Washington Seattle WA Ch
18
Hamilton paths and circuits in graphs
20
Hamilton paths and circuits in digraphs
28
Lenstra J K Eindhoven University of Technology Eindhoven and Centre
35
Lloyd E K University of Southampton Southampton Ch
44
Fundamental classes of graphs and digraphs
54
Automorphism Groups Isomorphism Reconstruction 1447
64
Special proof techniques for paths and circuits
69
Finite Sets and Relations
381
Probabilistic Methods 1785
385
Partially Ordered Sets
433
Matroids
481
Matroid Minors
527
Matroid Optimization and Algorithms
551
Symmetric Structures
611
Finite Geometries
647

Packings and coverings by paths and circuits
80
References
94
Combinatorial Optimization 1541
98
Connectivity and Network Flows
111
References
170
Computational Complexity 1599
173
Matchings and Extensions
179
Tools from Linear Algebra 1705
222
Combinatorial Games 2117
229
Colouring Stable Sets and Perfect Graphs
233
NowhereZero Flows
289
Embeddings and Minors
301
The History of Combinatorics 2163
308
Tools from Higher Algebra 1749
312
Random Graphs
351
Block Designs
693
Association Schemes
747
Codes
773
Combinatorial Structures in Geometry and Number Theory
809
Convex Polytopes and Related Complexes
875
Topological Methods 1819
896
Point Lattices
919
Combinatorics in Computer Science 2003
961
Combinatorial Number Theory
967
Combinatorics in Pure Mathematics 2039
1018
Author Index
xiii
Subject Index
lix
Ramsey Theory 1331
xcii
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