Homotopy types of Hom complexes of graph homomorphisms whose codomains are square-free
| Authors | |
|---|---|
| Year of publication | 2026 |
| Type | Article in Periodical |
| Magazine / Source | European Journal of Combinatorics |
| MU Faculty or unit | |
| Citation | |
| web | https://doi.org/10.1016/j.ejc.2025.104238 |
| Doi | https://doi.org/10.1016/j.ejc.2025.104238 |
| Keywords | Hom complex; Homotopy type; Poset topology; Square-free graph |
| Description | 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. |
| Related projects: |