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The Exact Number of Pentagons in Book-Free Graphs — arXiv:2611.06753

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.06753
License (as archived): CC0-1.0
Archived: 2026-11-05T18:28:35.340Z
SHA-256 of the archived text: d673ff844b694c981b7f20526120eb9793e078288628d13cfeafcb71973c1aa4
Stable URL of this page: https://metraipolis.com/documento/dc_b496caa75abc

How to cite

The Exact Number of Pentagons in Book-Free Graphs — arXiv:2611.06753 — arXiv (en), https://arxiv.org/abs/2611.06753 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b496caa75abc (Metraipolis archive dc_b496caa75abc, sha256 d673ff844b694c981b7f20526120eb9793e078288628d13cfeafcb71973c1aa4)

BibTeX

@misc{dcb496caa75abc,
  title = {The Exact Number of Pentagons in Book-Free Graphs — arXiv:2611.06753},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.06753},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b496caa75abc; sha256 d673ff844b694c981b7f20526120eb9793e078288628d13cfeafcb71973c1aa4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.06753. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $B_k$ denote the book consisting of $k$ triangles sharing a common edge. We prove that there exist absolute constants $\rho>0$ and $N$ such that, for every pair of integers $n,k$ with $n\ge N$ and $2\le k\le \rho n$, writing $n=5q+r$ with $0\le r<5$, \[ \operatorname{ex}(n,C_5,B_k)=q^{\,5-r}(q+1)^r, \] with the balanced complete $C_5$-blow-ups as the only extremal graphs. The linear order of this range is best possible since for all sufficiently large $n$, the formula fails whenever $k\ge0.14n$.

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/2611.06753 — 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 2026-11-05T18:18:34.001Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).