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An improved minimum degree threshold for fractional clique decompositions in partite graphs — arXiv:2611.08432

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.08432
License (as archived): CC0-1.0
Archived: 2026-11-06T14:52:53.938Z
SHA-256 of the archived text: 7b472abfc415ea7934b2669b16ea99daf1eaf9edb2ea9c23a607afe32e754f4d
Stable URL of this page: https://metraipolis.com/documento/dc_a985e07da153

How to cite

An improved minimum degree threshold for fractional clique decompositions in partite graphs — arXiv:2611.08432 — arXiv (en), https://arxiv.org/abs/2611.08432 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a985e07da153 (Metraipolis archive dc_a985e07da153, sha256 7b472abfc415ea7934b2669b16ea99daf1eaf9edb2ea9c23a607afe32e754f4d)

BibTeX

@misc{dca985e07da153,
  title = {An improved minimum degree threshold for fractional clique decompositions in partite graphs — arXiv:2611.08432},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.08432},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a985e07da153; sha256 7b472abfc415ea7934b2669b16ea99daf1eaf9edb2ea9c23a607afe32e754f4d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.08432. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove a Dirac-type condition for an $r$-partite graph to admit a fractional clique decomposition: every sufficiently large $r$-partite graph with $n$ vertices in each part and partite minimum degree at least $(1 - \frac{1}{30r^2}) n$ admits a fractional $K_r$-decomposition, subject to necessary divisibility conditions. This implies the same upper bound on the asymptotic minimum degree threshold for $r$-partite graphs to admit a $K_r$-decomposition, using a well-known reduction.

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/2611.08432 — 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 2026-11-06T14:24:27.850Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).