theorem Th99: :: CHORD:100

for G being _finite chordal _Graph
for a, b being Vertex of G st a <> b & not a,b are_adjacent holds
for S being VertexSeparator of a,b st S is minimal holds
for H being removeVertices of G,S
for a1 being Vertex of H st a = a1 holds
ex c being Vertex of G st
( c in H .reachableFrom a1 & ( for x being Vertex of G st x in S holds
c,x are_adjacent ) )