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Unbalanced spectral Turán problem for color-critical graphs with prescribed large maximum degree — arXiv:2609.01114

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.01114
License (as archived): CC0-1.0
Archived: 2026-10-17T07:06:22.365Z
SHA-256 of the archived text: 6e713af59bed7b78d6968c02a40666cf2f3fe94a658c66dcd3952e1832182c5c
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How to cite

Unbalanced spectral Turán problem for color-critical graphs with prescribed large maximum degree — arXiv:2609.01114 — arXiv (en), https://arxiv.org/abs/2609.01114 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_df235774ebce (Metraipolis archive dc_df235774ebce, sha256 6e713af59bed7b78d6968c02a40666cf2f3fe94a658c66dcd3952e1832182c5c)

BibTeX

@misc{dcdf235774ebce,
  title = {Unbalanced spectral Turán problem for color-critical graphs with prescribed large maximum degree — arXiv:2609.01114},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.01114},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_df235774ebce; sha256 6e713af59bed7b78d6968c02a40666cf2f3fe94a658c66dcd3952e1832182c5c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.01114. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $F$ be a connected color-critical graph with $\chi(F)=r+1\ge4$, let $S_{n,\Delta}^{(r)}=(n-\Delta)K_1\vee T(\Delta,r-1)$. We determine the graph of maximum adjacency spectral radius among all $n$-vertex $F$-free graphs with prescribed maximum degree $\Delta$. There is a constant $s_F\in[0,1)$ such that, for all sufficiently large $n$, $\left\lceil\frac{(r-1)n}{r}\right\rceil\le \Delta\le n-\Theta(n^{s_F})$ implies that every $n$-vertex $F$-free graph $G$ with $\Delta(G)=\Delta$ satisfies $\rho(G)\le \rho\bigl(S_{n,\Delta}^{(r)}\bigr)$, with equality if and only if $G\cong S_{n,\Delta}^{(r)}$. This is the spectral counterpart of the edge theorem of [European J. Combin. 106 (2022), 103576.] and extends the clique result in [ arXiv:2608.26634 , 2026.]. This result also provides a benchmark for unbalanced spectral Turán problems arising from other extremal parameters.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-02 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.01114 — 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 2026-10-17T06:52:59.689Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).