Treewidth of the generalized Kneser graphs
K Liu, M Cao, M Lu - arXiv preprint arXiv:2011.12725, 2020 - arxiv.org
K Liu, M Cao, M Lu
arXiv preprint arXiv:2011.12725, 2020•arxiv.orgLet $ n $, $ k $ and $ t $ be integers with $1\leq t< k\leq n $. The\emph {generalized Kneser
graph} $ K (n, k, t) $ is a graph whose vertices are the $ k $-subsets of a fixed $ n $-set,
where two $ k $-subsets $ A $ and $ B $ are adjacent if $| A\cap B|< t $. The graph $ K (n, k,
1) $ is the well-known\emph {Kneser graph}. In 2014, Harvey and Wood determined the
exact treewidth of the Kneser graphs for large $ n $ with respect to $ k $. In this paper, we
give the exact treewidth of the generalized Kneser graphs for $ t\geq2 $ and large $ n $ with …
graph} $ K (n, k, t) $ is a graph whose vertices are the $ k $-subsets of a fixed $ n $-set,
where two $ k $-subsets $ A $ and $ B $ are adjacent if $| A\cap B|< t $. The graph $ K (n, k,
1) $ is the well-known\emph {Kneser graph}. In 2014, Harvey and Wood determined the
exact treewidth of the Kneser graphs for large $ n $ with respect to $ k $. In this paper, we
give the exact treewidth of the generalized Kneser graphs for $ t\geq2 $ and large $ n $ with …
Let , and be integers with . The \emph{generalized Kneser graph} is a graph whose vertices are the -subsets of a fixed -set, where two -subsets and are adjacent if . The graph is the well-known \emph{Kneser graph}. In 2014, Harvey and Wood determined the exact treewidth of the Kneser graphs for large with respect to . In this paper, we give the exact treewidth of the generalized Kneser graphs for and large with respect to and . In the special case when , the graph usually denoted by which is the complement of the Johnson graph . We give a more precise result for the exact value of the treewidth of for any and .
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