## Tsukuba Journal of Mathematics

### Homotopy Type of the Box Complexes of Graphs without 4-cycles

Akira Kamibeppu

#### 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].

#### Article information

Source
Tsukuba J. Math., Volume 32, Number 2 (2008), 307-314.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165231

Digital Object Identifier
doi:10.21099/tkbjm/1496165231

Mathematical Reviews number (MathSciNet)
MR2477982

Zentralblatt MATH identifier
1187.05032

#### Citation

Kamibeppu, Akira. Homotopy Type of the Box Complexes of Graphs without 4-cycles. Tsukuba J. Math. 32 (2008), no. 2, 307--314. doi:10.21099/tkbjm/1496165231. https://projecteuclid.org/euclid.tkbjm/1496165231