Geodesic
Homotopy type of the independence complex of some categorical products of graphs
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 349-373.

Voir la notice de l'article provenant de la source International Press of Boston

It was conjectured by Goyal, Shukla and Singh that the independence complex of the categorical product $K_2 \times K_3 \times K_n$ has the homotopy type of a wedge of $(n-1)(3n-2)$ spheres of dimension $3$. Here we prove this conjecture by calculating the homotopy type of the independence complex of the graphs $C_{3r} \times K_n$ and $K_2 \times K_m \times K_n$. For $C_m \times K_n$ when $m$ is not a multiple of $3$, we calculate the homotopy type for $m = 4, 5$ and show that for other values it has to have the homotopy type of a wedge of spheres of at most $2$ consecutive dimensions and maybe some Moore spaces.
DOI : 10.4310/HHA.2024.v26.n2.a17
Classification : 05C76, 05E45, 55P10, 55P15
Keywords: independence complex, homotopy type 
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     title = {Homotopy type of the independence complex of some categorical products of graphs},
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Omar Antolín Camarena; Andrés Carnero Bravo. Homotopy type of the independence complex of some categorical products of graphs. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 349-373. doi : 10.4310/HHA.2024.v26.n2.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a17/

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