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On the representation number of chessboard graphs — arXiv:2609.22311

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.22311
License (as archived): CC0-1.0
Archived: 2026-10-09T21:44:32.567Z
SHA-256 of the archived text: 1dfda23dbf3e703c3c262052c83f8383a1c89206429fefb23ce3c0d8a6430362
Stable URL of this page: https://metraipolis.com/documento/dc_02facebb7449

How to cite

On the representation number of chessboard graphs — arXiv:2609.22311 — arXiv (en), https://arxiv.org/abs/2609.22311 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_02facebb7449 (Metraipolis archive dc_02facebb7449, sha256 1dfda23dbf3e703c3c262052c83f8383a1c89206429fefb23ce3c0d8a6430362)

BibTeX

@misc{dc02facebb7449,
  title = {On the representation number of chessboard graphs — arXiv:2609.22311},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.22311},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_02facebb7449; sha256 1dfda23dbf3e703c3c262052c83f8383a1c89206429fefb23ce3c0d8a6430362},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.22311. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The representation number of a graph is the smallest integer $k$ such that the graph can be represented by a word in which each vertex appears exactly $k$ times, and two distinct vertices $x$ and $y$ alternate in the word if and only if they are adjacent in the graph. We extend known results on the representation number for various graph classes to chessboard graphs - namely, king, queen, rook, bishop, and knight graphs. We provide a complete classification for queen graphs and partial classifications or observations for the other classes. As a consequence of our study, we obtain a characterization of all chessboard graphs that are circle graphs. Our work also leads to several interesting open problems.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-22 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.22311 — 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 2026-10-09T21:26:41.084Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).