5
Proof (cont’d)
•
Hardness: will design a structure A s.t. the set
{
f
| A
²
f
} is NP-hard.
•
By reduction from 3 colorability
•
•
A = ({0,1,2}, N), where N = {(i,j) | i
¹
j}
•
Let G = (V, E) be a graph, |V| = k
•
Define:
f
=
9
x
1
…
9
x
k
(
Æ
(x
i
, x
j
)
2
E
N(x
i
, x
j
))