Borel Homomorphisms from Forests to Kneser Graphs
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911469321322496 |
|---|---|
| author | Weilacher, Felix |
| author_facet | Weilacher, Felix |
| contents | We answer a recent question of Csóka and Vidnyánszky [arXiv:2407.10006] and give an alternate proof of one of their results. The subject of both is which finite graphs admit factor of i.i.d. homomorphisms from the 3-regular tree. We then give yet another proof of the result in the Borel setting which leads to the following: For each $d > 2$ and $k \in \mathbb{N}$, there is a Borel hyperfinite $d$-regular forest $G$ and a finite graph with chromatic number $k$, $H$, so that $G$ does not admit a Borel homomorphism to $H$. All of this is tied together by a focus on the case when the target graph $H$ is a (subgraph of a) Kneser graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19045 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Borel Homomorphisms from Forests to Kneser Graphs Weilacher, Felix Logic Combinatorics 03E15, 05C15, 05C72 We answer a recent question of Csóka and Vidnyánszky [arXiv:2407.10006] and give an alternate proof of one of their results. The subject of both is which finite graphs admit factor of i.i.d. homomorphisms from the 3-regular tree. We then give yet another proof of the result in the Borel setting which leads to the following: For each $d > 2$ and $k \in \mathbb{N}$, there is a Borel hyperfinite $d$-regular forest $G$ and a finite graph with chromatic number $k$, $H$, so that $G$ does not admit a Borel homomorphism to $H$. All of this is tied together by a focus on the case when the target graph $H$ is a (subgraph of a) Kneser graph. |
| title | Borel Homomorphisms from Forests to Kneser Graphs |
| topic | Logic Combinatorics 03E15, 05C15, 05C72 |
| url | https://arxiv.org/abs/2601.19045 |