Homotopy Type of Total Cut Complexes of Squared Cycle Graphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915577428180992 |
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| author | Shen, Yufeng Song, Zhiyu Yu, Fenglin Zhou, Leopold Wuhan Zhuang, Jingqi |
| author_facet | Shen, Yufeng Song, Zhiyu Yu, Fenglin Zhou, Leopold Wuhan Zhuang, Jingqi |
| contents | In this paper, we investigate the homotopy type and combinatorial properties of total cut complexes of squared cycle graphs. The total cut complexes are a new type of graphical complexes introduced by Bayer et al.(2024) to extend Fröberg's theorem. In Bayer et al.[Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2): 1630--1675 (2024)], the authors made a conjecture on the homotopy type of total cut complexes of squared cycle graphs for $k \geq 3$. We proved this conjecture in the case when $k=3$ . For general $k\geq 3$, we confirmed the cases when $n =3k+1$ and $3k+2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_22574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy Type of Total Cut Complexes of Squared Cycle Graphs Shen, Yufeng Song, Zhiyu Yu, Fenglin Zhou, Leopold Wuhan Zhuang, Jingqi Combinatorics Algebraic Topology 57M15, 57Q70, 05C69, 05E45 In this paper, we investigate the homotopy type and combinatorial properties of total cut complexes of squared cycle graphs. The total cut complexes are a new type of graphical complexes introduced by Bayer et al.(2024) to extend Fröberg's theorem. In Bayer et al.[Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2): 1630--1675 (2024)], the authors made a conjecture on the homotopy type of total cut complexes of squared cycle graphs for $k \geq 3$. We proved this conjecture in the case when $k=3$ . For general $k\geq 3$, we confirmed the cases when $n =3k+1$ and $3k+2$. |
| title | Homotopy Type of Total Cut Complexes of Squared Cycle Graphs |
| topic | Combinatorics Algebraic Topology 57M15, 57Q70, 05C69, 05E45 |
| url | https://arxiv.org/abs/2510.22574 |