. G . G u1, ,un, G , G:= G + u1 + + un .
v, u1, w, ,v G, v G, u1 G, u1 G. v u1 , G . w G, w {u1,,un}, u1 . , v w, u1 .
, v,u1,w, ,u,w, ,v w, w, v v, v,v, ,w,w, ,v u1, w, ,v . , G, v, , w. w G d(w) ≥ p/2+n , d(v) ≥ p/2+n. ( v) n+p-1. , :
n+p-1 = d(v)+d(V) ≥ d(w)+d(v) ≥ p/2+n+p/2+n = 2n+p.
, 0 ≥ n+1, , n > 0.
. G(V,E) n ≥ 3 u v :
d(u)+d(v) ≥ n (u,v) E, G .
G :
: d(vk) ≥ k+1 k < n/2.
: d(vi) ≤ i d(vk)≤ k => d(vi)+d(vk)≥n (k≠i)
: d(vk) ≤ k ≤ n/2 => d(vn-k) ≥ n-k.
, , ,
H(p) p , G(p) p . , , (, ) .
, , .
N = 8; d(vi) = 3; 3 ≥ 8/2 = 4 , : M = (1, 2, 3, 4, 5, 6, 7, 8, 1