Nov. 22, 2002

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Publications in Mathematics on Discrete Geometry:

BibTeX references.

Web links :


Digraphs: Theory, Algorithms, and Applications

Jørgen Bang-Jensen and Gregory Gutin

Springer, 2001

ToC

  1. Basic Terminology, Notation and Results (p.1)
  • Distances (p.45)
  • Flows in Networks (p.95)
  • Classes of Digraphs (p.171)
  • Hamiltonicity and Related Problems (p.227)
  • Hamiltonian Refinements (p.281)
  • Global Connectivity (p.345)
  • Orientations of Graphs (p.415)
  • Disjoint Paths and Trees (p.475)
  • Cycle Structure of Digraphs (p.545)
  • Generalizations of Digraphs (p.591)
  • Additional Topics (p.639)

  • Hypergraphs
    Combinatorics of finite sets

    Claude Berge

    Translated from the French.

    North-Holland Mathematical Library, vol. 45 (1989), 255 pages.


    Graphs and hypergraphs

    Claude Berge

    Translated from the French by Edward Minieka. Second revised edition.

    North-Holland Mathematical Library, vol. 6 (1976), 528 pages.


    The Foundations of Topological Graph Theory

    Bonnington, C.P. and Little, C.H.C.

    Springer-Verlag, 1995.


    Sphere Packing, Lattices and Groups

    J. H. Conway and N. J. A. Sloane

    Third edition, Springer-Verlag, NY, 1998
    Series: Grundlehren der mathematischen Wissenshaften, Volume 290; lxiv + 703 pp.

    Web: http://www.research.att.com/~njas/doc/splag.html

    From the cover: "The third edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the previous edition, the third edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. Of special interest to the third edition is a brief report on some recent developments in the field and an updated and enlarged Supplementary Bibliography with over 800 items."

    ToC

    1. Sphere Packings and Kissing Numbers.
  • Coverings, Lattices and Quantizers.
  • Codes, Designs, and Groups.
  • Certain Important Lattices and Their Properties.
  • Sphere Packing and Error-Correcting Codes.
  • Laminated Lattices.
  • Further Connections Between Codes and Lattices.
  • Algebraic Constructions for Lattices.
  • Bounds for Codes and Sphere Packings.
  • Three Lectures on Exceptional Groups.
  • The Golay Codes and the Mathieu Groups.
  • A Characterization of the Leech Lattice.
  • Bounds on Kissing Numbers.
  • Uniqueness of Certain Spherical Codes.
  • On the Classification of Integral Quadratic Forms.
  • Enumeration of Unimodular Lattices.
  • The 24-Dimensional Odd Unimodular Lattices.
  • Even Unimodular 24-Dimensional Lattices.
  • Enumeration of Extremal Self-Dual Lattices.
  • Finding the Closest Lattice Point.
  • Voronoi Cells of Lattices and Quantization Errors.
  • A Bound for the Covering Radius of the Leech Lattice.
  • The Covering Radius of the Leech Lattice.
  • Twenty-Three Constructions for the Leech Lattice.
  • The Cellular Structure of the Leech Lattice.
  • Lorenzian Forms for the Leech Lattice.
  • The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.
  • Leech Roots and Vinberg Groups.
  • The Monster Group and its 196885-Dimensional Space.
  • A Monster Lie Algebra?

  • Graph Theory and its Applications

    Jonathan Gross and Jay Yellen

    CRC Press, Boca Raton, Fla., USA, 1999.

    ToC

    1. Introduction to Graph Models (p.1)
  • Structure and Representation (p.47)
  • Trees (p.85)
  • Spanning Trees (p.123)
  • Connectivity (p.175)
  • Optimal Graph Traversals (p.203)
  • Graph Operations and Mappings (p.237)
  • Drawing Graphs and Maps (p.269)
  • Planarity of Graphs (p.303)
  • Graph Colorings (p.325)
  • Special Digraph Models (p.363)
  • Network Flows and Applications (p.399)
  • Graphical Enumeration (p.441)
  • Algebraic Specification of Graphs (p.475)
  • Nonplanar Layouts (p.509)
  • Weblink: http://www.graphtheory.com/


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    Page created & maintained by Frederic Leymarie, 2002.
    Comments, suggestions, etc., mail to: leymarie@lems.brown.edu