Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21877 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916033575518208 |
|---|---|
| author | Li, Heng Liu, Xizhi |
| author_facet | Li, Heng Liu, Xizhi |
| contents | The stability number of a forbidden family measures how many different structures are needed to approximate all near-extremal constructions avoiding it. An infinite stability number means that no finite list of structures suffices. We construct a simple explicit $3$-graph whose stability number is infinite. This extends the infinite-stability phenomenon for finite forbidden families, established by Hou--Li--Liu--Mubayi--Zhang, to the single-forbidden setting, and further develops the single-$3$-graph direction of Balogh--Clemen--Luo, in which exponentially many exact extremal constructions coexist with stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A single $3$-graph with infinite stability number Li, Heng Liu, Xizhi Combinatorics The stability number of a forbidden family measures how many different structures are needed to approximate all near-extremal constructions avoiding it. An infinite stability number means that no finite list of structures suffices. We construct a simple explicit $3$-graph whose stability number is infinite. This extends the infinite-stability phenomenon for finite forbidden families, established by Hou--Li--Liu--Mubayi--Zhang, to the single-forbidden setting, and further develops the single-$3$-graph direction of Balogh--Clemen--Luo, in which exponentially many exact extremal constructions coexist with stability. |
| title | A single $3$-graph with infinite stability number |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.21877 |