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KERNELS FOR THE F-DELETION PROBLEM
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DECLARATION I, hereby declare that
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I will be forever grateful to all t
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parameter tractable for every finit
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d
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F P {F}
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F F
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k
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c c = 5 c c = 5
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F i C(F i ) Q Q
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F i C(F i ) Q Q
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φ |x| k |x ′ | |x| L
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H H
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Deletion problem, Deletion we are a
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G M S G S
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+ +
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G H F H J k
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V(G)
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T i a, b, c V(T 1 )
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G χ(G) (G) +1 χ(G) G
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∨ ∧ ¬ ⇔ ⇒ ∀
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φ k φ 3 n
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C R N[C] ∩ R = ∅ E ′
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{u, v} N[u] =N[v]
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q q
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v ∈ A C(v) v v C(v)
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G A q H q = 1 ⎧
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G M ′ G M ′ k χ(G)
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⎫⎪ ⎬ ⎪ ⎭ N(v)
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Q S ⊆ A, N(T) ⊆ S T ⊆ B
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K 4 W n n
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⊲ (G, k)
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(G, k) u 1 ,u 2 ,...,u r
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→ G x x x k
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H r H
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C H v u
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S v Z v u v G
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v T W k X ⊆ W
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O(k 3 ) O(k 3
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|V(H)| H G \ H H
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t ⊕
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Π G t S t S
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f G T = {g | g : 2 X → {0, 1,
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Π n 1 G n V(G n
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t G S ⊆ V(G) (G ′ ,S
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X ′ b b b cc H
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⎧ ⎪⎨ V i V j V 1 V 2 ··
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v i y x ⎨ ⎩
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T \ S ′ |X(T i ′)| s T i v
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G \ X ∂(X) ={x, y, z} x z X
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C i A v v
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θ c θ c
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Y u ∈ X u ∈ Y u y
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F 20 2l5 (l×l) S
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F P K i,j
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F P ♦ H h (t × t)
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F P t : {b, x, y} {b, x, y}
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F P (G, k) (G) d S F
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F P (G, k) α (G) α
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F P G ∗ 0 H
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F P ⊲ µ(G)
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F P t r s t
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F P d ′ l > (k + d)d
- Page 129 and 130: F P β
- Page 131 and 132: F P k j (1)+k j (2)+...+ k j (2
- Page 133 and 134: F P (k √ log(k + d)) · (lo
- Page 135 and 136: F P
- Page 137 and 138: {F}
- Page 139 and 140: {F} ⎫ S } F |S| = (k) X (X
- Page 141 and 142: {F} F
- Page 143 and 144: {F} G k k G
- Page 145 and 146: Θ C O(k 2−ε ) coNP ⊆
- Page 147 and 148: Θ C • t s t H t H s
- Page 149 and 150: Θ C
- Page 151 and 152: Θ C (G, k) Θ c (G, k)
- Page 153 and 154: Θ C v H v θ c
- Page 155 and 156: Θ C v T ⊆ D c c = 5 S
- Page 157 and 158: Θ C G R \{v} G \{v}
- Page 159 and 160: Θ C (G, k) X := (G, k) G, k
- Page 161 and 162: Θ C O(k 2 log 3/2 k)
- Page 163 and 164: F G \ S S G \ S G[S] F
- Page 165 and 166: F {a, b, c, d,
- Page 167 and 168: F s p s
- Page 169 and 170: F e h H c[e] C
- Page 171 and 172: F F t G 1 G 2 G 1
- Page 173 and 174: F G 1 ⊕G 3 \Z F
- Page 175 and 176: F Q ∩ X i ⊆ ∂(X i ) Q
- Page 177 and 178: F O(n + m) =O(n 2 )
- Page 179: M θC ♦ H = Mθ 2
- Page 183 and 184: M θC v 1 v 2 ··· v s v s+1 ··
- Page 185 and 186: M θC G A G B X
- Page 187 and 188: M θC 2c 2
- Page 189 and 190: M θC S(G, µ(G)
- Page 191 and 192: M θC v S i ∩ S j = {v}, ∀
- Page 193 and 194: M θC u i x i u i
- Page 195 and 196: M θC
- Page 197 and 198: D(x) ∈ Q ′ i ∈ [t] :x i
- Page 199 and 200: P Q P Q P ppt Q
- Page 201 and 202: k k k
- Page 203 and 204: + k n O(k 3 )
- Page 205 and 206: c = 1 θ c k G
- Page 207 and 208: θ c c = 5 i v j v
- Page 209 and 210: w L k (w) ≠ l w 2 M
- Page 211 and 212: w = 1122312 ← y 2 1 1 2 2 3
- Page 213 and 214: C i (x p ,y p ) C j x
- Page 215 and 216: ⊆ /
- Page 217 and 218: ⊆ /
- Page 219 and 220: R ⊆ F ⋃ S∈R S = U
- Page 221 and 222: F i r r u i T
- Page 223 and 224: k k (T, k, c)
- Page 225 and 226: (T, k, c) (Q, c q ,k)
- Page 227 and 228: R R T(i)
- Page 229 and 230: T p T q l p ∈ V(T p )
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T =(V, E) (T, k, c, u)
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v v i (v i ,u i ) (u i ,u
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(S, T) S, T ⊆ V S ∩ T = ∅
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C H D C G D D H
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C(i) S k |S ∩ C(i)|
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⋆ F O(log 3/2 OPT) F
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n
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n
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+
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W[1]
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+ + +
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O( √ |V||E|)