Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Arana, Carmen, Stehlík, Matěj
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414969688
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