3
$\begingroup$

The permutahedron $\Pi_n$ is the polytope that is the convex hull of all permutations of the vector $(1,2,...,n)$. There are many results on its structure, but I couldn't find a result on the chromatic number of its 1-skeleton. Is it known?

Improve this question
$\endgroup$
1
  • 12
    $\begingroup$ It is bipartite; color a permutation with its sign. $\endgroup$
    – David E Speyer
    Jun 2, 2016 at 10:35

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.