Handbook of Combinatorics, Volume 1
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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University of Washington Seattle WA Ch
Hamilton paths and circuits in graphs
Hamilton paths and circuits in digraphs
Lenstra J K Eindhoven University of Technology Eindhoven and Centre
Lloyd E K University of Southampton Southampton Ch
Fundamental classes of graphs and digraphs
Automorphism Groups Isomorphism Reconstruction 1447
Special proof techniques for paths and circuits
Finite Sets and Relations
Probabilistic Methods 1785
Partially Ordered Sets
Matroid Optimization and Algorithms
Packings and coverings by paths and circuits
Combinatorial Optimization 1541
Connectivity and Network Flows
Computational Complexity 1599
Matchings and Extensions
Tools from Linear Algebra 1705
Combinatorial Games 2117
Colouring Stable Sets and Perfect Graphs
Embeddings and Minors
The History of Combinatorics 2163
Tools from Higher Algebra 1749
Combinatorial Structures in Geometry and Number Theory
Convex Polytopes and Related Complexes
Topological Methods 1819
Combinatorics in Computer Science 2003
Combinatorial Number Theory
Combinatorics in Pure Mathematics 2039
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