彩色多項式と彩色数 : ランダムな木の場合

Graph :

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

Chromatic Polynomial :

X^16 - 15 X^15 + 105 X^14 - 455 X^13 + 1365 X^12 - 3003 X^11 
+ 5005 X^10 - 6435 X^9 + 6435 X^8 - 5005 X^7 + 3003 X^6 
- 1365 X^5 + 455 X^4 - 105 X^3 + 15 X^2 - X

= (X) (X - 1)^15

Chromatic Number = 2