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| Autori principali: | , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2510.03698 |
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| _version_ | 1866915533504380928 |
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| author | Arana, Carmen Stehlík, Matěj |
| author_facet | Arana, Carmen Stehlík, Matěj |
| contents | The Lovász complex $L(G)$ of a graph $G$ is a deformation retract of its neighborhood complex, equipped with a canonical $Z_2$-action. We show that, under mild assumptions, $L(G)$ is homeomorphic to a surface if and only if $G$ is a non-bipartite quadrangulation of the orbit space $L(G)/Z_2$ in which every $4$-cycle is facial. This yields a classification of the Lovász complexes of all such quadrangulations. As an application, we contextualize a result of Archdeacon \emph{et al.}\ and Mohar and Seymour on the chromatic number of quadrangulations, obtaining a stronger statement about the $Z_2$-index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadrangulations and the Lovász complex Arana, Carmen Stehlík, Matěj Combinatorics The Lovász complex $L(G)$ of a graph $G$ is a deformation retract of its neighborhood complex, equipped with a canonical $Z_2$-action. We show that, under mild assumptions, $L(G)$ is homeomorphic to a surface if and only if $G$ is a non-bipartite quadrangulation of the orbit space $L(G)/Z_2$ in which every $4$-cycle is facial. This yields a classification of the Lovász complexes of all such quadrangulations. As an application, we contextualize a result of Archdeacon \emph{et al.}\ and Mohar and Seymour on the chromatic number of quadrangulations, obtaining a stronger statement about the $Z_2$-index. |
| title | Quadrangulations and the Lovász complex |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.03698 |