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arXiv · 2510.22574

Homotopy Type of Total Cut Complexes of Squared Cycle Graphs

Yufeng Shen·Zhiyu Song·Fenglin Yu·Leopold Wuhan Zhou·Jingqi Zhuang
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Abstract

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 Fr\"oberg'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 $3k+2$.

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Yufeng Shen, Zhiyu Song, Fenglin Yu, Leopold Wuhan Zhou, Jingqi Zhuang. 2025-10-26. Homotopy Type of Total Cut Complexes of Squared Cycle Graphs. https://arxiv.org/abs/2510.22574

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