MATH10200705001 Neeldhara Misra - Homi Bhabha National ...

(G, k)
G
v
v
v k
v ∈ V(G) H v ⊆ V(G) \{v}
v
v (k + 1) v
X ⊆ V(G) \{v} 2k v
H v v
q q =(k + 2)
(G, k) H v v
2k+(k+2)k 2k+(k+
2)k q q =(k + 2)
Greduction \ H v
v C 1 ,C 2 ,...,C r v
v H v
(G, k) k C i
C 1 ,C 2 ,...,C p
C p+1 ,...,C r
p k
p C i H v
u ∈ C i w ∈ H v (u, w) ∈ E(G)
H v
u C
H v G[C∪{v}] u ∈ C