On the treewidth of generalized q-Kneser graphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916251934130176 |
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| author | Metsch, Klaus |
| author_facet | Metsch, Klaus |
| contents | The generalized $q$-Kneser graph $K_q(n,k,t)$ for integers $k>t>0$ and $n>2k-t$ is the graph whose vertices are the $k$-dimensional subspaces of an $n$-dimensional $F_q$-vectorspace with two vertices $U_1$ and $U_2$ adjacent if and only if $\dim(U_1\cap U_2)<t$. We determine the treewidth of the generalized $q$-Kneser graphs $K_q(n,k,t)$ when $t\ge 2$ and $n$ is sufficiently large compared to $k$. The imposed bound on $n$ is a significant improvement of the previously known bound. One consequence of our results is that the treewidth of each $q$-Kneser graph $K_q(n,k,t)$ with $k>t>0$ and $n\ge 3k-t+9$ is equal to $\gauss{n}{k}-\gauss{n-t}{k-t}-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the treewidth of generalized q-Kneser graphs Metsch, Klaus Combinatorics 51D05, 51E20 The generalized $q$-Kneser graph $K_q(n,k,t)$ for integers $k>t>0$ and $n>2k-t$ is the graph whose vertices are the $k$-dimensional subspaces of an $n$-dimensional $F_q$-vectorspace with two vertices $U_1$ and $U_2$ adjacent if and only if $\dim(U_1\cap U_2)<t$. We determine the treewidth of the generalized $q$-Kneser graphs $K_q(n,k,t)$ when $t\ge 2$ and $n$ is sufficiently large compared to $k$. The imposed bound on $n$ is a significant improvement of the previously known bound. One consequence of our results is that the treewidth of each $q$-Kneser graph $K_q(n,k,t)$ with $k>t>0$ and $n\ge 3k-t+9$ is equal to $\gauss{n}{k}-\gauss{n-t}{k-t}-1$. |
| title | On the treewidth of generalized q-Kneser graphs |
| topic | Combinatorics 51D05, 51E20 |
| url | https://arxiv.org/abs/2405.11584 |