On a question of Erd\H{o}s and Ne\v{s}et\v{r}il about minimal cuts in a graph

TL;DR

This paper establishes an upper bound on the maximum number of inclusion-wise minimal vertex cuts in a graph with n vertices, answering a question posed by Erdős and Nešetřil.

Contribution

It provides a new exponential upper bound of approximately 1.89^n on the number of minimal vertex cuts, improving understanding of graph cut complexity.

Findings

Maximum number of minimal vertex cuts is at most 1.8899^n for large n.

Answers a longstanding question of Erdős and Nešetřil.

Advances bounds on graph cut enumeration.

Abstract

Answering a question of Erd\H{o}s and Ne\v{s}et\v{r}il, we show that the maximum number of inclusion-wise minimal vertex cuts in a graph on $n$ vertices is at most $1.8899^n$ for large enough $n$.