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# Kneser graphs

Let $k,n$ be positive integers with $k\leq n$. The *Kneser graph* $K_{{n:k}}$ has as its vertex set the $n\choose k$ $k$-element subsets of $\{1,2,\dots,n\}$. Two vertices are adjacent if and only if they correspond to disjoint subsets.

The graph $K_{{n:1}}$ is the complete graph on $n$ vertices. Another well-known Kneser graph is $K_{{5:2}}$, better known as the *Petersen graph*, which is shown in figure 1. The Petersen graph is often a counterexample to graph-theoretical conjectures.

Defines:

Petersen graph

Keywords:

Kneser graph, Petersen graph

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C99*no label found*

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