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arXiv · 2512.09674

Neighborhood Complexes of induced $k$-independent graphs

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

This paper is devoted to the neighborhood complexes of the induced $k$-independent graphs. Inspired by the surprising correspondence between total $k$-cut complex of $n$-cycle $C_n$ and neighborhood complex of stable Kneser graph $SG(n,k)$, we anticipate that the homotopy type of total cut complexes may have some relationships with the neighborhood complexes of induced $k$-independent graphs. We investigated the homotopy type of some total cut complexes and neighborhood complexes of some other graphs, using techniques from algebraic topology and discrete Morse theory.

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Yufeng Shen, Zhiyu Song, Feneglin Yu, Leopold Wuhan Zhou, Jingqi Zhuang. 2025-12-10. Neighborhood Complexes of induced $k$-independent graphs. https://arxiv.org/abs/2512.09674

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