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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.28082 |
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| _version_ | 1866913166899806208 |
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| author | Liu, Chang Niu, Ruichao Yang, Yuefeng |
| author_facet | Liu, Chang Niu, Ruichao Yang, Yuefeng |
| contents | Let $r_1$ and $r_2$ be positive integers with $r_1 \le r_2$. A graph $G$ is called $2$-DCC vertex $[r_1,r_2]$-pancyclic if, for any two distinct vertices of $G$ and any integer $\ell \in [r_1,r_2]$, there exist two vertex-disjoint cycles of lengths $\ell$ and $|V(G)|-\ell$, respectively, containing the two vertices separately. In this paper, we investigate the two-disjoint-cycle-cover vertex pancyclicity of the split-star network $S_n^2$. We prove that $S_n^2$ is $2$-DCC vertex $[3,n!/2]$-pancyclic for $n\ge4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-disjoint-cycle-cover vertex pancyclicity of split-star networks Liu, Chang Niu, Ruichao Yang, Yuefeng Combinatorics Let $r_1$ and $r_2$ be positive integers with $r_1 \le r_2$. A graph $G$ is called $2$-DCC vertex $[r_1,r_2]$-pancyclic if, for any two distinct vertices of $G$ and any integer $\ell \in [r_1,r_2]$, there exist two vertex-disjoint cycles of lengths $\ell$ and $|V(G)|-\ell$, respectively, containing the two vertices separately. In this paper, we investigate the two-disjoint-cycle-cover vertex pancyclicity of the split-star network $S_n^2$. We prove that $S_n^2$ is $2$-DCC vertex $[3,n!/2]$-pancyclic for $n\ge4$. |
| title | Two-disjoint-cycle-cover vertex pancyclicity of split-star networks |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.28082 |