Chromatic number of the n-cube

  • Level: Graduate 
  • Thread starter Dragonfall
  • Start date
3 replies · 6K views · last reply
Dragonfall
Messages
1,023
Reaction score
5
What is the chromatic number of the n-cube? As a graph, I mean. For the square and 3-cube, for example, it's 2.
 
The n-cube is bipartite, so its chromatic number is 2. If we label the vertices canonically with vectors in [tex]\{0, 1\}^n[/tex], then we can partition the vertices into those with an even number of 1's and those with an odd number of 1's.