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Peer-reviewedCC BY 4.0Discrete Mathematics

A note on highly connected K2,ℓ -minor free graphs

  • Nicolas Bousquet
  • Théo Pierron
  • Alexandra Wesolek
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Abstract

We show that every 3-connected K2,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 K2,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 K2,ℓ-minor free graphs.

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Cite

BibTeXRIS
BibTeX
@article{bousquet2026note,
  title = {{A note on highly connected $K_2,ℓ$ -minor free graphs}},
  author = {Nicolas Bousquet and Théo Pierron and Alexandra Wesolek},
  journal = {Discrete Mathematics},
  year = {2026},
  month = sep,
  doi = {10.1016/j.disc.2024.114005},
  url = {https://hal.science/hal-05745824v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A note on highly connected K_2,ℓ -minor free graphs
AU  - Nicolas Bousquet
AU  - Théo Pierron
AU  - Alexandra Wesolek
PY  - 2026
DA  - 2026/09/10
JO  - Discrete Mathematics
DO  - 10.1016/j.disc.2024.114005
UR  - https://hal.science/hal-05745824v1
AB  - 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.
SN  - 0012-365X
ER  -