Spectral extremal problems for degenerate graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908452741185536 |
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| author | Wu, Jiadong Kang, Liying Ni, Zhenyu |
| author_facet | Wu, Jiadong Kang, Liying Ni, Zhenyu |
| contents | A family of graphs is called degenerate if it contains at least one bipartite graph. In this paper, we investigate the spectral extremal problems for a degenerate family of graphs $\mathcal{F}$. By employing covering and independent covering of graphs, we establish a spectral stability result for $\mathcal{F}$. Using this stability result, we prove two general theorems that characterize spectral extremal graphs for a broad class of graph families $\mathcal{F}$ and imply several new and known results. Meanwhile, we establish the correlation between extremal graphs and spectral extremal graphs for $\mathcal{F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral extremal problems for degenerate graphs Wu, Jiadong Kang, Liying Ni, Zhenyu Combinatorics 05C50, 05C35 A family of graphs is called degenerate if it contains at least one bipartite graph. In this paper, we investigate the spectral extremal problems for a degenerate family of graphs $\mathcal{F}$. By employing covering and independent covering of graphs, we establish a spectral stability result for $\mathcal{F}$. Using this stability result, we prove two general theorems that characterize spectral extremal graphs for a broad class of graph families $\mathcal{F}$ and imply several new and known results. Meanwhile, we establish the correlation between extremal graphs and spectral extremal graphs for $\mathcal{F}$. |
| title | Spectral extremal problems for degenerate graphs |
| topic | Combinatorics 05C50, 05C35 |
| url | https://arxiv.org/abs/2507.12014 |