Skip to main content
SpringerLink
Log in

On Sets and Graphs

Perspectives on Logic and Combinatorics

  • Textbook
  • © 2017

Overview

Authors:
  1. Eugenio G. Omodeo

    1. DMG/DMI (Department of Mathematics and Geosciences, Section of Studies in Mathematics and Information Technology), University of Trieste, Trieste, Italy

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Alberto Policriti

    1. DMIF (Department of Mathematics Computer Science, and Physics), University of Udine, Udine, Italy

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Alexandru I. Tomescu

    1. Department of Computer Science Helsinki Institute for Information Technology HIIT, University of Helsinki, Helsinki, Finland

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Introduction

    • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
    Pages 1-27

  3. Basics

    1. Front Matter

      Pages 29-29
      Download chapter PDF

    2. Membership and Edge Relations

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 31-58

    3. Sets, Graphs, and Set Universes

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 59-97

  4. Graphs as Sets

    1. Front Matter

      Pages 99-99
      Download chapter PDF

    2. The Undirected Structure Underlying Sets

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 101-127

    3. Graphs as Transitive Sets

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 129-172

  5. Sets as Graphs

    1. Front Matter

      Pages 173-173
      Download chapter PDF

    2. Counting and Encoding Sets

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 175-199

    3. Random Generation of Sets

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 201-216

    4. Infinite Sets and Finite Combinatorics

      • Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
      Pages 217-250

  6. Back Matter

    Pages 251-275
    Download chapter PDF
Back to top

Keywords

About this book

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, problemsand insight panels.

Authors and Affiliations

  • DMG/DMI (Department of Mathematics and Geosciences, Section of Studies in Mathematics and Information Technology), University of Trieste, Trieste, Italy

    Eugenio G. Omodeo

  • DMIF (Department of Mathematics Computer Science, and Physics), University of Udine, Udine, Italy

    Alberto Policriti

  • Department of Computer Science Helsinki Institute for Information Technology HIIT, University of Helsinki, Helsinki, Finland

    Alexandru I. Tomescu

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.

Bibliographic Information

  • Book Title: On Sets and Graphs

  • Book Subtitle: Perspectives on Logic and Combinatorics

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

  • DOI: https://doi.org/10.1007/978-3-319-54981-1

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-54980-4Published: 22 May 2017

  • Softcover ISBN: 978-3-319-85536-3Published: 09 September 2018

  • eBook ISBN: 978-3-319-54981-1Published: 11 May 2017

  • Edition Number: 1

  • Number of Pages: XIX, 275

  • Number of Illustrations: 150 b/w illustrations

  • Topics: Logics and Meanings of Programs, Algorithm Analysis and Problem Complexity, Graph Theory, Combinatorics

Publish with us

Policies and ethics

Back to top

Search

Navigation