chromatic

  1. L

    Chromatic number

    what is the chromatic number of K(m,n) and Qn? my guess is X(Km,n)= n-1 and X(Qn)= 2^n but I needed to confirm that. thanks.
  2. E

    Edge chromatic number question (Graph theory)

    If G is a regular graph with an uneven number of vertices, prove that X'(G) = ?(G) + 1; where ?(G) is the maximum degree (in this case any degree) of G and X'(G) is the chromatic index (edge chromatic number).
  3. Solarmew

    Prove that f(x) is not a chromatic polynomial of any graph

    Prove that f(x) = x^6 - 12x^5 + 54x^4 - 112x^3 + 105x^2 - 36xis not a chromatic polynomial of any graph. no idea where to even begin :?
  4. Solarmew

    How to express a chromatic polynomial as a falling factorial

    How do i express a chromatic polynomial as a falling factorial function? [attachment=0:szbeqan8]Capture.JPG[/attachment:szbeqan8] I understand the join-product, but it seems that in order to apply it I'd need to convert the chromatic polynomials into falling factorial functions :? like...