On Sets and Graphs

Perspectives on Logic and Combinatorics

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

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English

Springer International Publishing AG
22 May 2017

Discrete mathematics; Combinatorics & graph theory; Algorithms & data structures; Mathematical theory of computation

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.

By: Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2017
Dimensions: Height: 235mm, Width: 155mm, Spine: 18mm
Weight: 5.679kg
ISBN: 9783319549804
ISBN 10: 3319549804
Pages: 275
Publication Date: 22 May 2017
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Introduction.- Part I: Basics.- Membership and Edge Relations.- Sets, Graphs, and Set Universes.- Part II: Graphs as Sets.- The Undirected Structure Underlying Sets.- Graphs as Transitive Sets.- Part III: Sets as Graphs.- Counting and Encoding Sets.- Random Generation of Sets.- Infinite Sets and Finite Combinatorics.- Appendix: Excerpts from a Referee-Checked Proof-Script.

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.