Informace o publikaci
Homotopy types of Hom complexes of graph homomorphisms whose codomains are square-free
| Autoři | |
|---|---|
| Rok publikování | 2026 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | European Journal of Combinatorics |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://doi.org/10.1016/j.ejc.2025.104238 |
| Doi | https://doi.org/10.1016/j.ejc.2025.104238 |
| Klíčová slova | Hom complex; Homotopy type; Poset topology; Square-free graph |
| Popis | Given finite simple graphs G and H, the Hom complex Hom(G,H) is a polyhedral complex having the graph homomorphisms G›H as the vertices. We determine the homotopy type of each connected component of Hom(G,H) when H is square-free, meaning that it does not contain the 4-cycle graph C4 as a subgraph. Specifically, for a connected G and a square-free H, we show that each connected component of Hom(G,H) is homotopy equivalent to a wedge sum of circles. We further show that, given any graph homomorphism f:G›H to a square-free H, one can determine the homotopy type of the connected component of Hom(G,H) containing f algorithmically. |
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