Handbook of CombinatoricsRonald L. Graham, Martin Grotschel, Martin Grötschel, László Lovász Combinatorics research, 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. The Handbook of Combinatoricsbrings together almost every aspect of this enormous field and is destined to become a classic. Ronald L. Graham, Martin Grotschel, and Laszlo Lovasz, three of the world's leading combinatorialists, have compiled a selection of articles that cover combinatorics in graph theory, theoretical computer science, optimization, and convexity theory, plus applications in operations research, electrical engineering, statistical mechanics, chemistry, molecular biology, pure mathematics, and computer science. The 20 articles in Volume 1 deal with structures while the 24 articles in Volume 2 focus on aspects, tools, applications, and horizons. |
Contents
Adam Mickiewicz University Poznań and Emory University | 6 |
University of Washington Seattle WA Ch | 18 |
Hamilton paths and circuits in graphs | 20 |
Lloyd E K University of Southampton Southampton Ch | 25 |
Hamilton paths and circuits in digraphs | 28 |
Fundamental classes of graphs and digraphs | 54 |
Automorphism Groups Isomorphism Reconstruction 1447 | 64 |
Special proof techniques for paths and circuits | 69 |
Partially Ordered Sets | 433 |
Matroids | 481 |
Matroid Minors | 527 |
Matroid Optimization and Algorithms | 551 |
Symmetric Structures | 611 |
Finite Geometries | 647 |
Block Designs | 693 |
Association Schemes | 747 |
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 |
Colouring Stable Sets and Perfect Graphs | 233 |
NowhereZero Flows | 289 |
Embeddings and Minors | 301 |
Tools from Higher Algebra 1749 | 312 |
Random Graphs | 351 |
Finite Sets and Relations | 381 |
Probabilistic Methods 1785 | 385 |
Codes | 773 |
Combinatorial Games 2117 | 788 |
Combinatorial Structures in Geometry and Number Theory | 809 |
The History of Combinatorics 2163 | 823 |
Klee and P Kleinschmidt | 880 |
Topological Methods 1819 | 896 |
Point Lattices | 919 |
Combinatorics in Computer Science 2003 | 961 |
Combinatorial Number Theory | 967 |
| 1018 | |
Author Index | xiii |
| lix | |
| xcii | |
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Common terms and phrases
3-connected a₁ algebraic algorithm association scheme b₁ binary bipartite graph blocks C₁ called chapter chromatic number colour Combin combinatorial components Comput conjecture connected graph construction convex Corollary cycle d-polytope decomposition defined degree denote digraph dimension Discrete Math disjoint dual elements embedding equivalent Erdős example exists finite function G₁ geometry graph G Graph Theory Hamilton circuit hamiltonian hypergraph incident induced inequality integer intersection isomorphic lattice least Lemma length Let G linear Lovász M₁ matrix matroid maximal maximum number minimum nodes obtained oriented matroids pairs partition path perfect graph perfect matching permutation groups Petersen graph planar graphs points polymatroid polynomial polytopes poset problem Proc projective plane proof proved random graph result S₁ simplicial stable set Steiner systems strongly regular graph subgraph submodular subset symmetric t₁ Theorem Thomassen tree Tutte v₁ vector vertex vertices x₁