Spectral extremal results on the $A_α$-spectral radius of graphs without $K_{a,b}$-minor
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929620592361472 |
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| author | Lei, Xingyu Li, Shuchao |
| author_facet | Lei, Xingyu Li, Shuchao |
| contents | An important theorem about the spectral Turán problem of $K_{a,b}$ was largely developed in separate papers. Recently it was completely resolved by Zhai and Lin [J. Comb. Theory, Ser. B 157 (2022) 184-215], which also confirms a conjecture proposed by Tait [J. Comb. Theory, Ser. A 166 (2019) 42-58]. Here, the prior work is fully stated, and then generalized with a self-contained proof. The more complete result is then used to better understand the relationship between the $A_α$-spectral radius and the structure of the corresponding extremal $K_{a,b}$-minor free graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral extremal results on the $A_α$-spectral radius of graphs without $K_{a,b}$-minor Lei, Xingyu Li, Shuchao Combinatorics 05C50, 05C83, 05C35 An important theorem about the spectral Turán problem of $K_{a,b}$ was largely developed in separate papers. Recently it was completely resolved by Zhai and Lin [J. Comb. Theory, Ser. B 157 (2022) 184-215], which also confirms a conjecture proposed by Tait [J. Comb. Theory, Ser. A 166 (2019) 42-58]. Here, the prior work is fully stated, and then generalized with a self-contained proof. The more complete result is then used to better understand the relationship between the $A_α$-spectral radius and the structure of the corresponding extremal $K_{a,b}$-minor free graph. |
| title | Spectral extremal results on the $A_α$-spectral radius of graphs without $K_{a,b}$-minor |
| topic | Combinatorics 05C50, 05C83, 05C35 |
| url | https://arxiv.org/abs/2412.06399 |