Abstract
In this paper, we show that a graph $G$ contains no 4-cycles if and only if $\Vert G \Vert$ is a strong $\mathbb{Z}_2$-deformation retract of the box complex $\Vert B(G) \Vert$ of $G$, where $G$ is the 1-dimensional free simplicial $\mathbb{Z}_{2}$-complex introduced in [2].
Citation
Akira Kamibeppu. "Homotopy Type of the Box Complexes of Graphs without 4-cycles." Tsukuba J. Math. 32 (2) 307 - 314, December 2008. https://doi.org/10.21099/tkbjm/1496165231
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