A formal approach to Menger's theorem

Menger's graph theorem equates the minimum size of a separating set for non-adjacent vertices a and b with the maximum number of disjoint paths between a and b. By capturing separating sets as models of an entailment relation, we take a formal approach to Menger's result. Upon showing that...

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Bibliographic Details
Published inReports on mathematical logic Vol. 57; no. 57; pp. 45 - 51
Main Authors Bonacina, Roberta, Misselbeck-Wessel, Daniel
Format Journal Article
LanguageEnglish
Published Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 01.01.2022
Jagiellonian University Press
Jagiellonian University-Jagiellonian University Press
Subjects
Apexes
Existence theorems
Logic
Philosophy of Science
entailment
Disjoint paths
separating set
inductive definition
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Summary:Menger's graph theorem equates the minimum size of a separating set for non-adjacent vertices a and b with the maximum number of disjoint paths between a and b. By capturing separating sets as models of an entailment relation, we take a formal approach to Menger's result. Upon showing that inconsistency is characterised by the existence of suficiently many disjoint paths, we recover Menger's theorem by way of completeness.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0137-2904
2084-2589
DOI:10.4467/20842589RM.22.003.16660