2011 - Départements

k i
Ci={Ci,1, . . . , Ci,`i}Ci,j
ci,j n
E`⊂Sk
i=1 Ci`
M
xi,j,` (Ci,j , `)

n
M
G= (V, E)n=|V|k
X k
xy G x ∈X y ∈X
G= (V, E)n=|V|k≥0
X k G
G X
G[V\X]
G k
k
k
k
f(k)
c > 0O(f(k)·nc)
xy k+1 x y
≤k
k+ 1
k2+ 1
≤k
k
O(k3)

G= (V, E)n=|V|
G
G= (V, E)n=|V|k
T G
k T
F⊂E G = (V, E)δF(x)
x F F x ∆(F) =
maxx∈VδF(x)F∆∗(G) ∆(T)
T G
∆∗(G)≤k
k≥∆(E)
(G, k)
k k
G(G, k)
k= 2
X⊂V G[V\X]t
∆∗(G)≥ dr+t−1
rer=|X|
X T G
T G (u, v)G\T
w T [u, v]δT(w)w T
max(δT(u), δT(v)) + 1
G T G
T0G∆(T0)≤
∆(T)T0∆(T)T
Sii T
G n c > 1i≥∆(T)−logcn
0<|Si−1| ≤ c|Si|
SiT t
Si−1G t
T c∆∗(G)+
dlogcne

D
p c(p)
p
c(p)
c(p) = D
p
c(p)>0
q
c(p)q6=p
c(q)q6=p
D= 3
s= (s1, s2, . . .)
i123456789101112131415161718. . .
si1 1 4 6 4 1 4 6 1 1 4 1 4 6 1 4 6 6 . . .
c(1) 1 2 2 2 2 3 2
c(4) 0 0 1 1 2 2 2
c(6) 0 0 0 1 1 1 1
s= (s1, s2, . . .)
Ip
j
i j (j+ 1)
c(p)
sic(p)

sic(p)
D(j+ 1)
I1
0= (1,2,6,7,8,9,10,11), I1 1= (12, . . .), . . .
I4
0= (3,5,13,14,15,16,17), . . .
I6
0= (4,18, . . .), . . .
Ip
jp
D+ 1
3D
s
Ip
j
D
p Ip
i
k
(G, k)n(G0, k0)
g(k)n(G, k)
G= (V, E)x y V
x y G
G
G
C1∪. . . ∪CkV x y
x y Ci
X G = (V, E)
G[X]X
E X
n
n−1G= (V, E)T
(V, T )T G x, y
G T [x, y]x y T
x y T