## You are here

HomeKneser graphs

## Primary tabs

# 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*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag