On Sets and Graphs

Perspectives on Logic and Combinatorics

Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu (Autoren)

Buch | Softcover

XIX, 275 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-85536-3 (ISBN)

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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.

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.

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.

Erscheinungsdatum	06.10.2018
Zusatzinfo	XIX, 275 p. 150 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	456 g
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	Algorithm analysis and problem complexity • Algorithmic Specification • combinatorial enumeration • combinatorics • graph theory • proof verification • set theory
ISBN-10	3-319-85536-0 / 3319855360
ISBN-13	978-3-319-85536-3 / 9783319855363
Zustand	Neuware