On the largest independent sets in the Kneser graph on chambers of PG(4,q)
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916267661721600 |
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| author | Heering, Philipp |
| author_facet | Heering, Philipp |
| contents | Let $Γ_4$ be the graph whose vertices are the chambers of the finite projective $4$-space PG(4,q), with two vertices being adjacent if the corresponding chambers are in general position. For $q\geq 749 $ we show that $α:=(q^2+q+1)(q^3+2q^2+q+1)(q+1)^2$ is the independence number of $Γ_4$ and the geometric structure of independent sets with $α$ vertices is described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the largest independent sets in the Kneser graph on chambers of PG(4,q) Heering, Philipp Combinatorics 05C69 (Primary) 51E20, 05B25 (Secondary) Let $Γ_4$ be the graph whose vertices are the chambers of the finite projective $4$-space PG(4,q), with two vertices being adjacent if the corresponding chambers are in general position. For $q\geq 749 $ we show that $α:=(q^2+q+1)(q^3+2q^2+q+1)(q+1)^2$ is the independence number of $Γ_4$ and the geometric structure of independent sets with $α$ vertices is described. |
| title | On the largest independent sets in the Kneser graph on chambers of PG(4,q) |
| topic | Combinatorics 05C69 (Primary) 51E20, 05B25 (Secondary) |
| url | https://arxiv.org/abs/2405.20891 |