MATH10200705001 Neeldhara Misra - Homi Bhabha National ...

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q q q = 1 (A ⊎ B) A S A q q 1 q A B B q · |A| q B A |B| q·m m (n − k)
Page 1 and 2: KERNELS FOR THE F-DELETION PROBLEM
Page 3 and 4: DECLARATION I, hereby declare that
Page 5 and 6: I will be forever grateful to all t
Page 7 and 8: parameter tractable for every finit
Page 9 and 10: d
Page 11 and 12: F P {F}
Page 13: F F
Page 16 and 17: k
Page 18 and 19: c c = 5 c c = 5
Page 20 and 21: F i C(F i ) Q Q
Page 22 and 23: F i C(F i ) Q Q
Page 24 and 25: φ |x| k |x ′ | |x| L
Page 26 and 27: H H
Page 28 and 29: Deletion problem, Deletion we are a
Page 30 and 31: G M S G S
Page 32 and 33: + +
Page 34 and 35: G H F H J k
Page 36 and 37: V(G)
Page 38 and 39: T i a, b, c V(T 1 )
Page 40 and 41: G χ(G) (G) +1 χ(G) G
Page 42 and 43: ∨ ∧ ¬ ⇔ ⇒ ∀
Page 44 and 45: φ k φ 3 n
Page 46 and 47: C R N[C] ∩ R = ∅ E ′
Page 48 and 49: {u, v} N[u] =N[v]
Page 52 and 53: Q H M
Page 54 and 55: Q q
Page 56 and 57: Q |B| |M| = k G[A
Page 58 and 59: Q e =(u, v) ∈ E(G)
Page 60 and 61: Q S ⊆ A, N(T) ⊆ S T ⊆ B
Page 62 and 63: k F k
Page 64 and 65: (G, k) H G ⋆ V(
Page 66 and 67: G {x 1 ,y 1 ,z},...,{x k+1 ,y
Page 68 and 69: H ⋆ V(H) =V(G) ⋆ (u, v) ∈
Page 70 and 71: v H x y
Page 72 and 73: (G, k) G
Page 74 and 75: v ⋆ H v ⋆
Page 76 and 77: v T W k X ⊆ W
Page 78 and 79: G ∆ c G
Page 80 and 81: +
Page 82 and 83: H X G (G \ H) ∪ ∗ X
Page 84 and 85: G G 1 G 2 t G 1 ,G 2 ∈ G
Page 86 and 87: f G f G (S) S
Page 88 and 89: f G T = {g | g : 2 X → {0, 1,
Page 90 and 91: c k G (G n ⊕ G, k)
Page 92 and 93: X ′ b b b cc H
Page 94 and 95: F
Page 96 and 97: G (d · bsp) (X,T) G
Page 98 and 99: G x z y G S ′
Page 100 and 101:
(2τ + 1) X τ X G τ
Page 102 and 103:
• C i T
Page 104 and 105:
θ c θ 9
Page 106 and 107:
S G\S H H ∈ F S
Page 108 and 109:
F 20 2l5 (l×l) S
Page 110 and 111:
F P
Page 112 and 113:
F H
Page 114 and 115:
(G) d F G d
Page 116 and 117:
β(t) =(H t ) >d t β
Page 118 and 119:
F (G, k) F
Page 120 and 121:
F d (d + 1)
Page 122 and 123:
n
Page 124 and 125:
G (k
Page 126 and 127:
δ s δ r (1 − 1/α)/2 δ s
Page 128 and 129:
t : {b, x, y} {b, x, y} {b, x, y
Page 130 and 131:
k j (1),k j (2),...,k j (2 j )
Page 132 and 133:
|S(G A , (S ∩ G A ))| + |S(G B ,
Page 134 and 135:
η O(log 3/2 n)
Page 136 and 137:
{F}
Page 138 and 139:
♦ X G τ τ X
Page 140 and 141:
X X S S X ∂(X) =
Page 142 and 143:
X V(G) \ S d G[X] d 20 2
Page 144 and 145:
Θ c θ c
Page 146 and 147:
θ c (2c−1) G ′
Page 148 and 149:
t : {b, x, y} {b, x, y} {b, x, y
Page 150 and 151:
v θ 5 k = 3
Page 152 and 153:
Gv ⎧⎪ ⎨ ⎪ ⎩ v G \ S (Gv)
Page 154 and 155:
v H v ⋆ ⋆
Page 156 and 157:
v ⋆ H v ⋆
Page 158 and 159:
(G, k) (G ∗ ,k ∗ )
Page 160 and 161:
|V(G ∗ )| < |V(G ′ )| k ∗ k
Page 162 and 163:
F
Page 164 and 165:
F G[B] G \
Page 166 and 167:
G I(H) 2 s h√ log h n
Page 168 and 169:
h H ∗ 2 h√ s log h h(h
Page 170 and 171:
H f H : V(H) → 2 [t] (u,
Page 172 and 173:
∂(G 2 ) R j G 1
Page 174 and 175:
(G, Y, k) P Π (G, T) T
Page 176 and 177:
n G m G F 11
Page 178 and 179:
M θc
Page 180 and 181:
V(G)
Page 182 and 183:
G 2c 2 k 2 G k θ c G
Page 184 and 185:
P i j C ⊆ P
Page 186 and 187:
⊲ µ(H t ) t µ(H r )+µ(
Page 188 and 189:
µ(G) =1 G θ c θ c
Page 190 and 191:
{θ C } θ c G k k
Page 192 and 193:
{θ C } V(G) \{v}
Page 194 and 195:
{θ C }
Page 196 and 197:
⊆ /
Page 198 and 199:
k G k k G k
Page 200 and 201:
x A z ∈ A NP f(x) =y
Page 202 and 203:
(W, k) W = w 1 ···w n {0,
Page 204 and 205:
θ c ⊆ /
Page 206 and 207:
{θ C } c 3 θ c
Page 208 and 209:
{θ C } G k θ c
Page 210 and 211:
⊆ /
Page 212 and 213:
Q (u p ,s p
Page 214 and 215:
G M S G S
Page 216 and 217:
⊆ /
Page 218 and 219:
U F = {F 1 ,F 2 ,...,F n } U
Page 220 and 221:
R ′′ . R ′′ (U
Page 222 and 223:
u j T ′′ .
Page 224 and 225:
Q T T(i) T(j) v[
Page 226 and 227:
i ∈ [k + 1] ∀{u, v} ∈ T(i) (u
Page 228 and 229:
G =(V, E)
Page 230 and 231:
T R T V(R) T(T
Page 232 and 233:
(T, k, c) T {v 1 ,v 2 ,..
Page 234 and 235:
(T, v, c, k) T =(V, E) s
Page 236 and 237:
u ∈ C(i) w ∈ C(j) j ≠ i
Page 238 and 239:
C(i) S k |S ∩ C(i)|
Page 240 and 241:
F F F
Page 242 and 243:
F ♦ F F ♦
Page 244 and 245:
n
Page 246 and 247:
+
Page 248 and 249:
k O(n 2 )
Page 250 and 251:
+
Page 252 and 253:
O( √ |V||E|)
Page 254:
O( √ |V||E|)
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MATH10200705001 Neeldhara Misra - Homi Bhabha National ...

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