彩色多項式と彩色数 : K_4, K_5 の和グラフの場合

Graph :

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

Chromatic Polynomial :

X^9 - 16 X^8 + 106 X^7 - 376 X^6 + 769 X^5 - 904 X^4 + 564 X^3 - 144 X^2

= (X)^2 (X - 1)^2 (X - 2)^2 (X - 3)^2 (X - 4)

Chromatic Number = 5