MATH10200705001 Neeldhara Misra - Homi Bhabha National ...

t G S ⊆ V(G)
(G ′ ,S ′ ) ∈ H t ζ Π G ((G′ ,S ′ )) P Π (G ⊕ G ′ ,S ∪ S ′ )
|S| ζ Π G ((G′ ,S ′ )) + f(t)
+ p
+ Π
c G k r
X G |X| >c O(|X|) G ∗ =(V ∗ ,E ∗ )
k ∗ |V(G ∗ )| < |V(G)| k ∗ k (G ∗ ,k ∗ ) ∈ Π
(G, k) ∈ Π
S (Π,2r) c = max Y∈S |Y| ζ
2r 2c S
2r H 2c H ≡ Π ζ(H) η
2r 2c N
2r H ′ k ′
(H ⊕ H ′ ,k+ η(H)) ∈ Π ⇐⇒ (ζ(H) ⊕ H ′ ,k) ∈ Π.
|X| >2c 2r X ′ ⊆ X c