2009

G= (X, E)n m
T(X, T )
x G e = (x, y)x
x
G e
G F
F n/2
G
F
G G/F G
F G/F
(X, F )G/F
G(X, F )
F
G/F G
G O(mlog n)
n
pi

ai,j i j
ak=Pi6=kak,i k
k pk+ak
pk+ak
k piai,j
X={s, t}∪{i|1≤i≤n, i 6=k}∪{(i, j)|1≤i < j ≤n, i 6=k, j 6=k}
R⊂ {1,2, . . . , n} \ {k}
R
m(R) = X
i∈R
pi+1
2X
i,j∈R
ai,j .
R k
m(R)/|R|> pk+akk
k
R k
m(R)/|R|> pk+ak
R
G= (X, E)S
G S
G

G= (X, E)S⊂X
k
T k
x y S x y T
Y3n C ={C1, . . . , Cm}
Y i Ci⊂Y|Ci|= 3
C0C
Y C0Y
G= (X, E)S X k
Y=S1∪S2∪S3SiS
C(x, y, z)S1×S2×S3G
b3k/|Y|c G x y z
Y|Y|= 3n C Y
X={x0} ∪ C∪Y E ={(x0, c)|c∈
C}∪{(c, y)|c∈C, y ∈Y}S={x0} ∪ Y
k= 4n
G S GS
S x y S (x, y)
x y G
GS
S G