彩色多項式と彩色数 : 完全グラフ K_9 の場合

Graph :

 0 1 1 1 1 1 1 1 1
 1 0 1 1 1 1 1 1 1
 1 1 0 1 1 1 1 1 1
 1 1 1 0 1 1 1 1 1
 1 1 1 1 0 1 1 1 1
 1 1 1 1 1 0 1 1 1
 1 1 1 1 1 1 0 1 1
 1 1 1 1 1 1 1 0 1
 1 1 1 1 1 1 1 1 0

Chromatic Polynomial :

X^9 - 36 X^8 + 546 X^7 - 4536 X^6 + 22449 X^5 - 67284 X^4 + 118124 X^3 
- 109584 X^2 + 40320 X

= (X) (X - 1) (X - 2) (X - 3) (X - 4) (X - 5) (X - 6) (X - 7) (X - 8)

Chromatic Number = 9