AI Chat AI Image Generator AI Video Text to Speech

A note on highly connected K_2,ℓ-minor free graphs

01/05/2023

∙

by Nicolas Bousquet, et al.

∙

∙

We show that every 3-connected K_2,ℓ-minor free graph with minimum degree at least 4 has maximum degree at most 7ℓ. As a consequence, we show that every 3-connected K_2,ℓ-minor free graph with minimum degree at least 5 and no twins of degree 5 has bounded size. Our proofs use Steiner trees and nested cuts; in particular, they do not rely on Ding's characterization of K_2,ℓ-minor free graphs.

Nicolas Bousquet
43 publications
Théo Pierron
17 publications
Alexandra Wesolek
7 publications

page 1

page 2

page 3

page 4

research

∙ 10/10/2022

Spanning trees of smallest maximum degree in subdivisions of graphs

Given a graph G and a positive integer k, we study the question wheth...

0 Christoph Brause, et al. ∙

research

∙ 09/02/2023

Characterising 4-tangles through a connectivity property

Every large k-connected graph-minor induces a k-tangle in its ambient gr...

0 Johannes Carmesin, et al. ∙

research

∙ 02/28/2023

Improved bounds on the cop number when forbidding a minor

Andreae (1986) proved that the cop number of connected H-minor-free grap...

0 Franklin Kenter, et al. ∙

research

∙ 11/02/2017

Minor-free graphs have light spanners

We show that every H-minor-free graph has a light (1+ϵ)-spanner, resolvi...

0 Glencora Borradaile, et al. ∙

research

∙ 04/04/2023

VC Set Systems in Minor-free (Di)Graphs and Applications

A recent line of work on VC set systems in minor-free (undirected) graph...

0 Hung Le, et al. ∙

research

∙ 02/23/2021

Testing Hamiltonicity (and other problems) in Minor-Free Graphs

In this paper we provide sub-linear algorithms for several fundamental p...

0 Reut Levi, et al. ∙

research

∙ 06/21/2020

Further progress towards Hadwiger's conjecture

In 1943, Hadwiger conjectured that every graph with no K_t minor is (t-1...

0 Luke Postle, et al. ∙