theorem Th82: :: GLIB_008:82

for G being _finite simple connected _Graph ex p being non empty Graph-yielding _finite simple connected FinSequence st
( p . 1 is _trivial & p . 1 is edgeless & p . (len p) = G & len p = G .order() & ( for n being Element of dom p st n <= (len p) - 1 holds
ex v being object ex V being non empty finite set st
( v in (the_Vertices_of G) \ (the_Vertices_of (p . n)) & V c= the_Vertices_of (p . n) & p . (n + 1) is addAdjVertexAll of p . n,v,V ) ) )