Homotopy Type of the Box Complexes of Graphs without 4-cycles
Akira Kamibeppu · Tsukuba Journal of Mathematics · 2008
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].