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Minimum-degree thresholds beyond bounded colourability — arXiv:2610.39759

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.39759
License (as archived): CC0-1.0
Archived: 2026-11-01T02:37:59.818Z
SHA-256 of the archived text: 9fc23d21466c8c16c86a77dc4920f4b2bb16c686edd9f5f2d2c3ad161c05eeb3
Stable URL of this page: https://metraipolis.com/documento/dc_71cb2422d2da

How to cite

Minimum-degree thresholds beyond bounded colourability — arXiv:2610.39759 — arXiv (en), https://arxiv.org/abs/2610.39759 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_71cb2422d2da (Metraipolis archive dc_71cb2422d2da, sha256 9fc23d21466c8c16c86a77dc4920f4b2bb16c686edd9f5f2d2c3ad161c05eeb3)

BibTeX

@misc{dc71cb2422d2da,
  title = {Minimum-degree thresholds beyond bounded colourability — arXiv:2610.39759},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.39759},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_71cb2422d2da; sha256 9fc23d21466c8c16c86a77dc4920f4b2bb16c686edd9f5f2d2c3ad161c05eeb3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.39759. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We survey recent developments on minimum-degree thresholds in extremal graph theory, with an emphasis on structural refinements of the chromatic-threshold problem. The chromatic threshold asks when a linear minimum-degree condition forces bounded chromatic number in an \(H\)-free graph; its complete classification shows a striking finite trichotomy. We discuss several stronger and related threshold notions in which bounded colourability is replaced by bounded \(H\)-free homomorphic images, bounded neighbourhood complexity via VC-dimension, exact blowup structure for maximal \(H\)-free graphs, and improved quantitative bounds in graph removal lemmas. In contrast with the rigidity of the chromatic threshold, these newer parameters exhibit richer behaviour, including separations from \(\delta_\chi(H)\), new exact values, accumulation points in fixed-chromatic spectra, positivity phenomena for 3-chromatic graphs, asymmetric variants, and failures of monotonicity.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.39759 — 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 2026-11-01T02:15:28.283Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).