On Sets and Graphs

Perspectives on Logic and Combinatorics

Nonfiction, Science & Nature, Mathematics, Graphic Methods, Computers, General Computing, Programming
Cover of the book On Sets and Graphs by Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu, Springer International Publishing
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Author: Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu ISBN: 9783319549811
Publisher: Springer International Publishing Publication: May 11, 2017
Imprint: Springer Language: English
Author: Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu
ISBN: 9783319549811
Publisher: Springer International Publishing
Publication: May 11, 2017
Imprint: Springer
Language: English

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.

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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, problems and insight panels.

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