Minimum Separators and Menger’s Theorem

Abstract

Menger’s theorem implies simply the following property: A minimum separator S of non-adjacent vertices u and v in a graph G remains a minimum uv-separator in G- e , for every e∈ E(G[ S] ) . In this paper, we prove the equivalence between Menger’s theorem and this property and so by given an elementary proof of it, we get a new proof of Menger’s theorem. © 2023, The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature.