Chromatic number of the n-cube

  • Thread starter Thread starter Dragonfall
  • Start date Start date
AI Thread Summary
The chromatic number of the n-cube is established as 2, indicating that it is a bipartite graph. For both the square and the 3-cube, this holds true, supported by empirical evidence. The vertices of the n-cube can be labeled using vectors in {0, 1}^n, allowing for a clear partition based on the parity of the number of 1's. This bipartite nature confirms that only two colors are needed for proper vertex coloring. Thus, the discussion concludes that the chromatic number of the n-cube is definitively 2.
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.
 
Mathematics news on Phys.org
Empirical evidence suggests it's just 2.
 
The n-cube is bipartite, so its chromatic number is 2. If we label the vertices canonically with vectors in \{0, 1\}^n, then we can partition the vertices into those with an even number of 1's and those with an odd number of 1's.
 
Oh ya, thanks.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Higher Dimensional Spheres viz. Cubes
Replies
1
Views
1K
B Difference between powers of numbers equaling 1
Replies
11
Views
2K
I Finding the chromatic number of a graph with biconnected components
Replies
1
Views
2K
B Cuboids in a Cube: {##1,n##} Dim. n
Replies
20
Views
2K
B Cube Math: How Many Smaller Cubes in a Larger Cube?
Replies
4
Views
3K
I A way to comprehend the geometry of a hypercube
Replies
2
Views
2K
B 1lb cube of 99% pure copper?
Replies
10
Views
2K
B Need some clarification to get dimensions for a volume
Replies
5
Views
2K
MHB Sum of Numbers on Cube Faces to Equal 2004
Replies
1
Views
2K
Insights Fermat's Last Theorem
3
Replies
105
Views
6K

Hot Threads

Recent Insights

Back
Top