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$K_h$-Minor-Free Graphs Have Balanced Separators of Size $O(h\sqrt{n})$ — arXiv:2611.00663

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00663
License (as archived): CC0-1.0
Archived: 2026-11-03T18:49:30.121Z
SHA-256 of the archived text: bdca0d0255439badd630d710d3ef731c5df9e9f9787b6ab656968f43f5815a85
Stable URL of this page: https://metraipolis.com/documento/dc_8ce06ff410ee

How to cite

$K_h$-Minor-Free Graphs Have Balanced Separators of Size $O(h\sqrt{n})$ — arXiv:2611.00663 — arXiv (en), https://arxiv.org/abs/2611.00663 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_8ce06ff410ee (Metraipolis archive dc_8ce06ff410ee, sha256 bdca0d0255439badd630d710d3ef731c5df9e9f9787b6ab656968f43f5815a85)

BibTeX

@misc{dc8ce06ff410ee,
  title = {$K_h$-Minor-Free Graphs Have Balanced Separators of Size $O(hsqrtn)$ — arXiv:2611.00663},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00663},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_8ce06ff410ee; sha256 bdca0d0255439badd630d710d3ef731c5df9e9f9787b6ab656968f43f5815a85},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00663. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We show that every $K_h$-minor-free graph with $n$ vertices has a balanced separator of size $O(h\sqrt{n})$ for any parameter $h \in \mathbb{N}$, resolving the conjecture posed by Alon, Seymour, and Thomas [AST90] in 1990. The proof is elementary, building on the combinatorial framework by Le [Le26]. A key new idea of the proof is the existence of a short hitting walk on vertex expanders: given $k$ large (not necessarily disjoint) subsets of vertices, there is a walk of length $O(k/\psi(G))$ hitting every subset, where $\psi(G)$ is the vertex expansion. This technical result substantially improves on an analogous lemma by Alon, Seymour, and Thomas [AST90] in an important parameter setting, where the previous lower bound [Kot00] does not apply.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO) ; Discrete Mathematics (cs.DM).
Pagina del lavoro: https://arxiv.org/abs/2611.00663 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:15:38.047Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).