Turán Number of Subdivisions of Multipartite Graphs
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912420972199936 |
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| author | Liu, Xiao-Chuan Peng, Danni Yang, Xu |
| author_facet | Liu, Xiao-Chuan Peng, Danni Yang, Xu |
| contents | In this paper, we investigate the Turán exponent for $1$-subdivisions of graphs that are neither bipartite nor complete. Specifically, we establish an upper bound on the Turán number of the 1-subdivision of $K_{s,t}^+$, where $K_{s,t}^+$ is obtained by adding a single edge within the part of size $s$ of the complete bipartite graph $K_{s,t}$, with $4\leq s \leq t$. In addition, we derive an upper bound for the extremal number of a family of graphs formed by (possibly degenerate) 1-subdivisions of certain tripartite graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_13119 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Turán Number of Subdivisions of Multipartite Graphs Liu, Xiao-Chuan Peng, Danni Yang, Xu Combinatorics 05C35 In this paper, we investigate the Turán exponent for $1$-subdivisions of graphs that are neither bipartite nor complete. Specifically, we establish an upper bound on the Turán number of the 1-subdivision of $K_{s,t}^+$, where $K_{s,t}^+$ is obtained by adding a single edge within the part of size $s$ of the complete bipartite graph $K_{s,t}$, with $4\leq s \leq t$. In addition, we derive an upper bound for the extremal number of a family of graphs formed by (possibly degenerate) 1-subdivisions of certain tripartite graphs. |
| title | Turán Number of Subdivisions of Multipartite Graphs |
| topic | Combinatorics 05C35 |
| url | https://arxiv.org/abs/2112.13119 |