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On the achromatic index of Johnson graphs $J(n,2)$ — arXiv:2608.05056

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.05056
License (as archived): CC0-1.0
Archived: 2026-10-31T11:46:05.502Z
SHA-256 of the archived text: f93f53f2c0f23a31d3467fe16a9bf882218989082a998bf071088e3553280839
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How to cite

On the achromatic index of Johnson graphs $J(n,2)$ — arXiv:2608.05056 — arXiv (en), https://arxiv.org/abs/2608.05056 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_35c85beffd97 (Metraipolis archive dc_35c85beffd97, sha256 f93f53f2c0f23a31d3467fe16a9bf882218989082a998bf071088e3553280839)

BibTeX

@misc{dc35c85beffd97,
  title = {On the achromatic index of Johnson graphs $J(n,2)$ — arXiv:2608.05056},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.05056},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_35c85beffd97; sha256 f93f53f2c0f23a31d3467fe16a9bf882218989082a998bf071088e3553280839},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.05056. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we study proper and complete edge-colorings of Johnson graphs $J(n,2)$, also called $n$-triangular graphs. They are isomorphic both to the 2-token graphs of complete graphs and to the line graphs of complete graphs. A $t$-edge-coloring of a graph $G$ is a function that assigns one color from $\{1,2,\ldots,t\}$ to each edge. Such a coloring is called proper if no two incident edges receive the same color, and complete if every pair of distinct colors appears on a pair of incident edges. The achromatic index, denoted by $\alpha_2(G)$, is the largest integer $t$ for which $G$ admits a proper and complete $t$-edge-coloring. We establish new lower and upper bounds for $\alpha_2(J(n,2))$, provide explicit proper and complete edge-colorings attaining the lower bounds, and determine the exact value of $\alpha_2(J(n,2))$ for several values of $n$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-06 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.05056 — 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 2026-10-31T11:35:10.110Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-06?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).