
theorem Th102:
  for G being _finite chordal _Graph ex v being Vertex of G st v is simplicial
proof
  let G be _finite chordal _Graph;
  per cases;
  suppose
A1: G is complete;
    set u = the Vertex of G;
    u is simplicial by A1,Th63;
    hence thesis;
  end;
  suppose
A2: not G is complete;
    then not G is _trivial;
    then ex a,b being Vertex of G st a<>b &( not a,b are_adjacent) & a is
    simplicial & b is simplicial by A2,Th101;
    hence thesis;
  end;
end;
