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Graphs and Order

The Role of Graphs in the Theory of Ordered Sets and Its Applications

  • Book
  • © 1985

Overview

Editors:
  1. Ivan Rival

    1. Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

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Part of the book series: Nato Science Series C: (ASIC, volume 147)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-xix
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  2. Graph Representations

    1. Front Matter

      Pages 1-1
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    2. Comparability Graphs

      • David Kelly
      Pages 3-40

    3. Algorithmic Aspects of Comparability Graphs and Interval Graphs

      • Rolf H. Möhring
      Pages 41-101

    4. The Diagram

      • Ivan Rival
      Pages 103-133

  3. Scheduling, Searching and Sorting

    1. Front Matter

      Pages 135-135
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    2. The Information Theoretic Bound for Problems on Ordered Sets and Graphs

      • Michael Saks
      Pages 137-168

    3. Sorting and Graphs

      • Béla Bollobás, Pavol Hell
      Pages 169-184

    4. A Graph-Theoretic Approach to the Jump-Number Problem

      • Maciej M. Syslo
      Pages 185-215

    5. Acyclic Subdigraphs and Linear Orderings: Polytopes, Facets, and a Cutting Plane Algorithm

      • M. Grötschel, M. Jünger, G. Reinelt
      Pages 217-264

  5. Social Sciences

    1. Front Matter

      Pages 413-413
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    2. Issues in the Theory of Uniqueness in Measurement

      • Fred S. Roberts
      Pages 415-444

  6. Decomposition

    1. Front Matter

      Pages 445-445
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    2. Path-Partitions in Directed Graphs and Posets

      • Claude Berge
      Pages 447-464

  7. Recursion

    1. Front Matter

      Pages 465-465
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    2. Recursion Theoretic Aspects of Graphs and Orders

      • James H. Schmerl
      Pages 467-484
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Keywords

About this book

This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved.

Reviews

` The volume provides an excellent introduction to many aspects of graphs and order. On the whole, the papers are well written and they provide a huge amount of information. Certainly I am glad to have Graphs and Order now as part of my library and suggest that it would provide an excellent source and reference that ought to find its way into at least every departmental library. '
The Journal of Symbolic Logic

Editors and Affiliations

  • Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

    Ivan Rival

Bibliographic Information

  • Book Title: Graphs and Order

  • Book Subtitle: The Role of Graphs in the Theory of Ordered Sets and Its Applications

  • Editors: Ivan Rival

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-009-5315-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland. 1985

  • Hardcover ISBN: 978-90-277-1943-0Published: 28 February 1985

  • Softcover ISBN: 978-94-010-8848-0Published: 13 October 2011

  • eBook ISBN: 978-94-009-5315-4Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: 816

  • Topics: Order, Lattices, Ordered Algebraic Structures, Discrete Mathematics in Computer Science

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