彩色多項式と彩色数 : 閉路 C_5, C_6 の場合

Graph :

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

Chromatic Polynomial :

X^5 - 5 X^4 + 10 X^3 - 10 X^2 + 4 X

= (X) (X - 1) (X - 2) (X^2 - 2 X + 2)

Chromatic Number = 3

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Graph :

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

Chromatic Polynomial :

X^6 - 6 X^5 + 15 X^4 - 20 X^3 + 15 X^2 - 5 X

= (X) (X - 1) (X^4 - 5 X^3 + 10 X^2 - 10 X + 5)

Chromatic Number = 2