The spectral radius of $1$-planar graphs without complete subgraphs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912764573777920 |
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| author | Xu, Weilun Chang, An |
| author_facet | Xu, Weilun Chang, An |
| contents | A 1-planar graph refers to a graph that can be drawn on the plane such that each edge has at most one crossing. In this paper, focusing on the spectral Turán-type problems of $1$-planar graphs, we determine completely the unique spectral extremal graph among all $K_3$-free or $K_4$-free $1$-planar graphs, and provide a characterization of the spectral extremal graphs for $K_5$-free $1$-planar graphs, confining the candidates to a specific, small family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The spectral radius of $1$-planar graphs without complete subgraphs Xu, Weilun Chang, An Combinatorics 05C10, 05C50 G.2.2 A 1-planar graph refers to a graph that can be drawn on the plane such that each edge has at most one crossing. In this paper, focusing on the spectral Turán-type problems of $1$-planar graphs, we determine completely the unique spectral extremal graph among all $K_3$-free or $K_4$-free $1$-planar graphs, and provide a characterization of the spectral extremal graphs for $K_5$-free $1$-planar graphs, confining the candidates to a specific, small family. |
| title | The spectral radius of $1$-planar graphs without complete subgraphs |
| topic | Combinatorics 05C10, 05C50 G.2.2 |
| url | https://arxiv.org/abs/2512.12909 |