Turán extremal graphs vs. Signless Laplacian spectral Turán extremal graphs
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914324218380288 |
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| author | Chen, Ming-Zhu Jin, Ya-Lei Zhang, Peng-Li Zhang, Xiao-Dong |
| author_facet | Chen, Ming-Zhu Jin, Ya-Lei Zhang, Peng-Li Zhang, Xiao-Dong |
| contents | Let $F$ be a graph with chromatic number $χ(F) = r+1$. Denote by $ex(n, F)$ and $Ex(n, F)$ the Turán number and the set of all extremal graphs for $F$, respectively. In addition, $ex_{ssp}(n, F)$ and $Ex_{ssp}(n, F)$ are the maximum signless Laplacian spectral radius of all $n$-vertex $F$-free graphs and the set of all $n$-vertex $F$-free graphs with signless Laplacian spectral radius $ex_{ssp}(n, F)$, respectively. It is known that $Ex_{ssp}(n, F)\supset Ex(n, F)$ if $F$ is a triangle. In this paper, employing the regularity method and Füredi's stability theorem, we prove that for a given graph $F$ and $r\geqslant 3$, if $ex(n, F) = t_r(n)+O(1)$, then $ Ex_{ssp}(n, F) \subseteq Ex(n, F)$ for sufficiently large $n$, where $t_r(n)$ is the number of edges in the Turán graph $T_r(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Turán extremal graphs vs. Signless Laplacian spectral Turán extremal graphs Chen, Ming-Zhu Jin, Ya-Lei Zhang, Peng-Li Zhang, Xiao-Dong Combinatorics 05C50, 05C35 Let $F$ be a graph with chromatic number $χ(F) = r+1$. Denote by $ex(n, F)$ and $Ex(n, F)$ the Turán number and the set of all extremal graphs for $F$, respectively. In addition, $ex_{ssp}(n, F)$ and $Ex_{ssp}(n, F)$ are the maximum signless Laplacian spectral radius of all $n$-vertex $F$-free graphs and the set of all $n$-vertex $F$-free graphs with signless Laplacian spectral radius $ex_{ssp}(n, F)$, respectively. It is known that $Ex_{ssp}(n, F)\supset Ex(n, F)$ if $F$ is a triangle. In this paper, employing the regularity method and Füredi's stability theorem, we prove that for a given graph $F$ and $r\geqslant 3$, if $ex(n, F) = t_r(n)+O(1)$, then $ Ex_{ssp}(n, F) \subseteq Ex(n, F)$ for sufficiently large $n$, where $t_r(n)$ is the number of edges in the Turán graph $T_r(n)$. |
| title | Turán extremal graphs vs. Signless Laplacian spectral Turán extremal graphs |
| topic | Combinatorics 05C50, 05C35 |
| url | https://arxiv.org/abs/2602.11502 |