Kneser graph

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Chromatic number

{ n − 2 k + 2 n ≥ 2 k 1 n < 2 k {\displaystyle {\begin{cases}n-2k+2&n\geq 2k\\1&n<2k\end{cases}}}

Edges

1 2 ( n k ) ( n − k k ) {\displaystyle {\frac {1}{2}}{\binom {n}{k}}{\binom {n-k}{k}}}

Named after

Martin Kneser

Notation

K(n, k), KGn,k.

Properties

( n − k k ) {\displaystyle {\tbinom {n-k}{k}}} -regular arc-transitive

Vertices

( n k ) {\displaystyle {\binom {n}{k}}}