Kneser graph

In graph theory, the Kneser graph K(n, k) (alternatively KG_n,k) is the graph whose vertices correspond to the k-element subsets of a set of n elements, and where two vertices are adjacent if and only if the two corresponding sets are disjoint. Kneser graphs are named after Martin Kneser, who first investigated them in 1956.

Kneser graph
The Kneser graph K(5, 2), isomorphic to the Petersen graph
Named after	Martin Kneser
Vertices	${\displaystyle {\binom {n}{k}}}$
Edges	${\displaystyle {\frac {1}{2}}{\binom {n}{k}}{\binom {n-k}{k}}}$
Chromatic number	${\displaystyle {\begin{cases}n-2k+2&n\geq 2k\\1&n<2k\end{cases}}}$
Properties	${\displaystyle {\tbinom {n-k}{k}}}$-regular arc-transitive
Notation	K(n, k), KGn,k.
Table of graphs and parameters