On an induced version of Menger's theorem

TL;DR

This paper extends Menger's theorem to graphs with bounded degree and excluding topological minors, providing new bounds and a tight result for two paths, including computer-assisted proof for the latter.

Contribution

It introduces Menger-type results with non-adjacent paths in specialized graph classes and improves bounds, especially for subcubic graphs, with a precise two-path result.

Findings

Established Menger-type theorems for graphs excluding topological minors.

Derived better bounds for graphs with maximum degree three.

Provided a computer-assisted proof for the tight two-path case.

Abstract

We prove Menger-type results in which the obtained paths are pairwise non-adjacent, both for graphs of bounded maximum degree and, more generally, for graphs excluding a topological minor. We further show better bounds in the subcubic case, and in particular obtain a tight result for two paths using a computer-assisted proof.