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On Sets and Graphs

Perspectives on Logic and Combinatorics

Authors: Omodeo, Eugenio G., Policriti, Alberto, Tomescu, Alexandru I.

  • Presents a unified view of sets and graphs and their use for natural representation of finite structures
  • Casts combinatorial issues arising at the core of different disciplines in clear computational terms
  • Illustrates automatically computer-checked proof scenarios, made available on the Web
  • Provides a light introduction to formal methods without assuming any prior knowledge
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eBook 47,59 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-54981-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 56,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-54980-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels.

About the authors

Dr. Eugenio G. Omodeo is a professor in the Department of Mathematics and Geosciences at the University of Trieste, Italy. His other publications include the Springer title Computational Logic and Set Theory.

Dr. Alberto Policriti is a Professor of Computer Science in the Department of Mathematics, Computer Science, and Physics at the University of Udine, Italy. Together with Dr. Eugenio G. Omodeo, he is co-author of the Springer title Set Theory for Computing.

Dr. Alexandru I. Tomescu is a postdoctoral researcher in the Department of Computer Science at the University of Helsinki, Finland.

Table of contents (8 chapters)

  • Introduction

    Omodeo, Eugenio G. (et al.)

    Pages 1-27

    Preview Buy Chapter 24,95 €
  • Membership and Edge Relations

    Omodeo, Eugenio G. (et al.)

    Pages 31-58

    Preview Buy Chapter 24,95 €
  • Sets, Graphs, and Set Universes

    Omodeo, Eugenio G. (et al.)

    Pages 59-97

    Preview Buy Chapter 24,95 €
  • The Undirected Structure Underlying Sets

    Omodeo, Eugenio G. (et al.)

    Pages 101-127

    Preview Buy Chapter 24,95 €
  • Graphs as Transitive Sets

    Omodeo, Eugenio G. (et al.)

    Pages 129-172

    Preview Buy Chapter 24,95 €

Buy this book

eBook 47,59 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-54981-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 56,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-54980-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
On Sets and Graphs
Book Subtitle
Perspectives on Logic and Combinatorics
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-54981-1
DOI
10.1007/978-3-319-54981-1
Hardcover ISBN
978-3-319-54980-4
Edition Number
1
Number of Pages
XIX, 275
Number of Illustrations and Tables
150 b/w illustrations
Topics