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Well-Covered Powers: Cartesian Products and Cayley Graphs — arXiv:2611.03956

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03956
License (as archived): CC0-1.0
Archived: 2026-11-04T19:00:15.646Z
SHA-256 of the archived text: 5d89639947a9d72e551dd70485d27367dfa1bc029497e72b09bc3ebbcdfe5d99
Stable URL of this page: https://metraipolis.com/documento/dc_7670faaa7dab

How to cite

Well-Covered Powers: Cartesian Products and Cayley Graphs — arXiv:2611.03956 — arXiv (en), https://arxiv.org/abs/2611.03956 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7670faaa7dab (Metraipolis archive dc_7670faaa7dab, sha256 5d89639947a9d72e551dd70485d27367dfa1bc029497e72b09bc3ebbcdfe5d99)

BibTeX

@misc{dc7670faaa7dab,
  title = {Well-Covered Powers: Cartesian Products and Cayley Graphs — arXiv:2611.03956},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03956},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7670faaa7dab; sha256 5d89639947a9d72e551dd70485d27367dfa1bc029497e72b09bc3ebbcdfe5d99},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03956. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study graphs whose powers are well-covered, with an emphasis on Cartesian products and Cayley graphs. We first establish necessary conditions and sufficient criteria for Cartesian products, provide examples showing that a factor need not be well-covered and that two noncomplete factors can have the well-covered powers property, and classify several structured product families. In particular, we construct graphs satisfying the well-covered powers property for arbitrarily large diameters. We then show that the Cartesian square of a connected abelian Cayley graph is well-covered exactly when the graph is complete. We classify the well-covered-power graphs among connected circulant graphs of degree at most four. For Cartesian products of any number of complete graphs, we also prove that the recursive alphabet-size inequalities in the final conjecture are sufficient for all powers to be well-covered, prove partial converses for arbitrarily many factors, and give explicit obstructions for every binary prefix followed by one complete factor.

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/2611.03956 — 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 2026-11-04T18:38:22.303Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).