, Kn , Kn n .
Kn = (X, U). , , ,
(n) = , (17.18)
n ³ 4. . K4: P(K4) = 1, P(K5) = 5, P(K6) = 15.
, .
( ) :
(17.19)
. ( (17.19)) .
. Kn, , . Kn, U\U.., , .. U1, x 1 , U2, x 2 , U3, x 3, .. , Kn, n = 6 . 17.18.
. 17.18. K 6
(Kn) 4. , (17.18), :
min(6) = 3.
.
Kn . n n(n 1)/2 Kn . n(n 1)/2 n , .. n(n 3)/2 .
:
U i = { u (i, i + 2), u (i - 1, i + 3),..., u (i - q + 1, i + q + 1)},
(17.20)
i = 1, i - 1 = n, i - 2 = n 1,....
, U i , .
U i . , U i U i . i , U i +1, U i +1, .
, , ,
(17.21)
, , . , UL+1, . , n n , . n - , .
|
|
Kn .
Kn (n = 8) :
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | |||
R8 = | 1 | 0 | × | 1 | × | , | ||||||||||
2 | 0 | × | 1 | 1 | 1 | × | ||||||||||
3 | 0 | × | 1 | 1 | 1 | × | ||||||||||
4 | 0 | × | 1 | × | ||||||||||||
5 | 0 | × | × | |||||||||||||
6 | 0 | × | × | |||||||||||||
7 | 0 | × | × | |||||||||||||
8 | 0 |
K8, R8, (. 17.19).
. 17.19. K 8
:
U1 (1,7)(2,6)(3,5), U5 (1,3)(5,7)(4,8),
U2 (2,7)(3,6), U6 (1,4)(8,5),
U3 (2,8)(3,7)(4,6), U7 (2,4)(1,5)(8,6),
U4 (3,8)(4,7), U8 (1,6)(2,5).
U1, U2, U3, U4 , . (17.21), L = 4 U5, U6, U7, U8 , .
(K8) = 18, (17.19) ( 9 9 ).
, Pmin(G) . (17.21). . .
, R11. (17.21) , .
,
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 1 | 2 | 3 | 4 | 5 | |||
1 | 0 | × | 1 | × | . | |||||||||||||
2 | 0 | × | 1 | 1 | 1 | × | ||||||||||||
3 | 0 | × | 1 | 1 | 1 | 1 | 1 | × | ||||||||||
4 | 0 | × | 1 | 1 | 1 | 1 | 1 | 1 | × | |||||||||
R11 = | 5 | 0 | × | 1 | 1 | 1 | 1 | 1 | × | |||||||||
6 | 0 | × | 1 | 1 | 1 | × | ||||||||||||
7 | 0 | × | 1 | |||||||||||||||
8 | 0 | × | ||||||||||||||||
9 | 0 | × | ||||||||||||||||
10 | 0 | × | ||||||||||||||||
11 | 0 | × |
.
|
. (17.19) K11 :
.
, Kn . Kn Pn,min. , n, , xi, xj (i, j Î I = {1, 2,..., n}, i Ï j). , xi, , , xj. .
, 4 . 4 . Kn
. (17.22)
Kn Kn-1, .
.
, R8 , , . :
1 | 2 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 4 | 5 | 6 | |||
R7 = | 1 | 0 | × | 1 | × | . | ||||||||
2 | 0 | × | 1 | 1 | 1 | × | ||||||||
4 | 0 | × | 1 | 1 | × | |||||||||
5 | 0 | × | × | |||||||||||
6 | 0 | × | × | |||||||||||
7 | 0 | × | × | |||||||||||
8 | 0 | × |
R7 K7.
(17.19)
.
Kn n
. (17.23)
(17.23)
(17.24)
n º 0 (mod 2) n ³ 6.
Kn n ¹ 0 (mod 2) (17.22).
. (17.25)
(17.23) xi Pmax Kn Kn-1 .
(17.25) (17.22)
. (17.26)
(17.26)
(17.27)
n ¹ 0 (mod 2) n ³ 7.
(17.24) (17.27) ,
. (17.28)
|
|
(3.28)
n , (17.29)
n , (17.30)
, (17.19) .
, .
.1. . , , .
.2. . . . . : . ..
.3. . , . . . G. G , , , , . , , . , .
.
1. .
2. .
3. .
4. .
5. .
6. ?
7. ?
8. .
9. .
10. .