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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2508.03746 |
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Table des matières:
- For a cycle $C_k$ on $k$ vertices, its $p$-th power, denoted $C_k^p$, is the graph obtained by adding edges between all pairs of vertices at distance at most $p$ in $C_k$. Let $\ex(n, F)$ and $\spex(n, F)$ denote the maximum possible number of edges and the maximum possible spectral radius, respectively, among all $n$-vertex $F$-free graphs. In this paper, we determine precisely the unique extremal graph achieving $\ex(n, C_k^p)$ and $\spex(n, C_k^p)$ for sufficiently large $n$.