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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2604.14763 |
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| _version_ | 1866911597898760192 |
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| author | Cai, Yiting Guo, Haiyan Lai, Hong-Jian Zhou, Bo |
| author_facet | Cai, Yiting Guo, Haiyan Lai, Hong-Jian Zhou, Bo |
| contents | The Hamiltonicity and related subjects of split graphs, and in particular $K_{1,r}$-free split graphs with $r\ge 3$ received much attention. Dai et al. [Discrete Math. 345 (2022) 112826] conjectured that every $(r-1)$-connected $K_{1,r}$-free split graph is Hamiltonian. They proved the case when $r=4$, and earlier Renjith and Sadagopan [Int. J. Found. Comput. Sci. 33 (2022) 1--32] proved the case when $r=3$. Recently, Liu, Song, Zhang and Lai [Discrete Math. 346 (2023) 113402] proved that a split graph is Hamiltonian if and only if it is fully cycle extendable. So for $r=3,4$ every $(r-1)$-connected $K_{1,r}$-free split graph is fully cycle extendable. We give tight spectral sufficient conditions for a $K_{1,r}$-free split graph to be Hamiltonian for $r=3,4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14763 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tight spectral conditions for the Hamiltonicity of $K_{1,r}$-free split graphs Cai, Yiting Guo, Haiyan Lai, Hong-Jian Zhou, Bo Combinatorics The Hamiltonicity and related subjects of split graphs, and in particular $K_{1,r}$-free split graphs with $r\ge 3$ received much attention. Dai et al. [Discrete Math. 345 (2022) 112826] conjectured that every $(r-1)$-connected $K_{1,r}$-free split graph is Hamiltonian. They proved the case when $r=4$, and earlier Renjith and Sadagopan [Int. J. Found. Comput. Sci. 33 (2022) 1--32] proved the case when $r=3$. Recently, Liu, Song, Zhang and Lai [Discrete Math. 346 (2023) 113402] proved that a split graph is Hamiltonian if and only if it is fully cycle extendable. So for $r=3,4$ every $(r-1)$-connected $K_{1,r}$-free split graph is fully cycle extendable. We give tight spectral sufficient conditions for a $K_{1,r}$-free split graph to be Hamiltonian for $r=3,4$. |
| title | Tight spectral conditions for the Hamiltonicity of $K_{1,r}$-free split graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.14763 |