2006

G1,2, . . . , n
n−1
E=E1∪E2∪. . . ∪En−1Ei∩Ej=∅i6=j
T E
(T1) T
(T2) T
n−1T
T=∅
e T
T T := T∪ {e}
E1={e1, e5}, E2={e2, e4}, E3={e3}
4
12
34
e1
e2
e3
e5
e
T k < n −1 (T1) (T2)

GT= (X∪Y, A)
E={e1, . . . , em}G X eiT Y
ejT A GT
x∈X y ∈Y(x, y)∈A x y x
T
x∈X y ∈Y(y, x)∈A T −y+x
GT
X1X
T X2X
T
X1∩X2T
X=X1∪X2
GT
T0(T1),(T2)T
(T1),(T2)
k n
G= (X, E)X E
G S ⊂X
X\S S
G
G
S0S0
d(x, y)n
d(x, y)≤d(x, z) + d(z, y) (x, y, z)
k n
d
S k
φ(S) = max
y /∈Smin
x∈Sd(x, y).
φ∗minS⊂Vφ(S)

G= (X, E)KX
X
d(x, y) = (1{x, y} ∈ E,
2
k
k d n S k
φ(S)<2φ∗P = NP
E=
{1,2, . . . , n} F F1, F2, . . . , FmE
E i k
FiFi, i ∈I
Si∈IFi=E
Fixi
n0≤xi≤1
E={1,2,3,4,5}F1={1,3,5}, F2={2,3,4}, F3=
{1,2}, F4={4,5}, F5={1,2,4}, F6={3,5}
ˆx1,ˆx2,...,ˆxm
ˆx1,ˆx2,...,ˆxm
ˆx1,ˆx2,...,ˆxmi∈Iˆxi
ˆx1,ˆx2,...,ˆxmj
Fj1, Fj2, . . . , FjkFii∈I
j Fi, i ∈I1−1
e
mlog(n)O(log n)
1
2