# The chromatic polynomial of the hyper cube graph $Q_4$?

I need to research cube graphs for problems in evolutionary biology. To that end I have generated a few 100,000 graphs on the 4-cube. However, I want to double check that my list is correct. To that end it would be handy to have the chromatic polynomial. By evaluating the polynomial at $x=-1$ one finds the number of Directed Acyclic Graphs on the 4-cube, according to a result by Stanley.

Does anyone know the chromatic polynomial of the hyper cube graph $Q_4$?

• Posted also on MO: Chromatic polynomial for hyper cube. I think that this answer gives a very reasonable advice about cross-posting. And there are several other discussions about cross-posting on meta. Jun 21, 2017 at 13:51
• Dear Martin Sleziak, my question was put on hold. I have no clue why. I added context, but that did not help from my understanding. My best guess is that my question sorts under "research" rather than a student question. For that reason I asked the same question in mathoverflow. I greatly appreciate the answer I got, by the way. Jun 22, 2017 at 10:50
• If you think that the question is worth reopening, you can try to make your case in the reopen request thread. Jun 23, 2017 at 10:42

## 1 Answer

WolframAlpha returns

$$x(x - 1) (x^{14} - 31 x^{13} + 465 x^{12} - 4471 x^{11} + 30793 x^{10} - 160807 x^9 + 657229 x^8 - 2137667 x^7 + 5564285 x^6 - 11536667 x^5 + 18740317 x^4 - 23081607 x^3 + 20308039 x^2 - 11372201 x + 3040575)$$

probably using the usual deletion-contraction method.