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A formal approach to Menger's theorem

Bonacina Roberta, Misselbeck-Wessel Daniel

Reports on Mathematical Logic

2022

Vol. 57

45--51

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 sufficiently many disjoint paths, we recover Menger’s theorem by way of completeness.