## Handbook of CombinatoricsCombinatorics 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 Combinatorics brings 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. |

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### Contents

Adam Mickiewicz University Poznań and Emory University | 6 |

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 |

Random Graphs | 351 |

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 |

Special proof techniques for paths and circuits | 69 |

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 |

Finite Geometries | 647 |

Block Designs | 693 |

Association Schemes | 747 |

Codes | 773 |

Combinatorial Structures in Geometry and Number Theory | 809 |

Convex Polytopes and Related Complexes | 877 |

Topological Methods 1819 | 896 |

Point Lattices | 919 |

Combinatorics in Computer Science 2003 | 961 |

Combinatorial Number Theory | 967 |

1018 | |

Author Index | xiii |

lix | |

xcii | |

### Other editions - View all

Handbook of combinatorics. 2 (1995), Volume 2 Ronald L. Graham,Martin Grötschel,László Lovász No preview available - 1995 |

### Common terms and phrases

3-connected algorithm applications bipartite blocks bound called chapter circuit colour Combin combinatorial complete components Comput condition conjecture connected consider construction contains convex corresponding covering cycle defined denote determined digraph dimension directed Discrete Math disjoint distance dual edges elements equal equivalent Erdős example exists extended finite flow function geometry given gives graph G groups Hamilton Hence holds hypergraph implies incident independent induced inequality integer intersection known lattice least Lemma length Let G linear Lovász matching Math matrix matroid maximal maximum minor nodes Note obtained pairs partition path perfect permutation planar plane points polynomial polytopes poset positive possible problem projective proof proved regular representation respectively result satisfies simple space structure subgraph subset Suppose Theorem Theory tree vector vertex vertices weight

### References to this book

Projective Geometries Over Finite Fields James William Peter Hirschfeld,Reader in Mathematics James Hirschfeld No preview available - 1998 |

Projective Geometries Over Finite Fields James William Peter Hirschfeld,Reader in Mathematics James Hirschfeld No preview available - 1998 |