
theorem :: Theorem 4.3, Golumbic p. 86
  for G being _finite chordal _Graph holds (((LexBFS:CSeq(G)).Result())`1
  )" is perfect VertexScheme of G
proof
  let G be _finite chordal _Graph;
  set Hh = ((LexBFS:CSeq(G)).Result())`1;
  reconsider V = Hh" as VertexScheme of G by Th50;
A1: dom Hh = the_Vertices_of G by Th49;
  Hh = (LexBFS:CSeq(G))``1.Result() by Th40;
  then Hh is one-to-one by Th18;
  then
A2: V" = Hh by FUNCT_1:43;
  Hh is with_property_L3 by Th53;
  hence thesis by A1,A2,Th54;
end;
