On an Induced Version of Menger's Theorem

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. More precisely, we show the existence of a constant $C$, depending only on the maximum degree or on the forbidd...

Full description

Saved in:
Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 31; no. 4
Main Authors Hendrey, Kevin, Norin, Sergey, Steiner, Raphael, Turcotte, Jérémie
Format Journal Article
LanguageEnglish
Published 01.11.2024
Online AccessGet full text

Cover

More Information
Summary: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. More precisely, we show the existence of a constant $C$, depending only on the maximum degree or on the forbidden topological minor, such that for any pair of sets of vertices $X,Y$ and any positive integer $k$, there exists either $k$ pairwise non-adjacent $X\text{-}Y$-paths, or a set of fewer than $Ck$ vertices which separates $X$ and $Y$. We further show better bounds in the subcubic case, and in particular obtain a tight result for two paths using a computer-assisted proof.
ISSN:1077-8926
1077-8926
DOI:10.37236/12575