reserve E,V for set, G,G1,G2 for _Graph, c,c1,c2 for Cardinal, n for Nat;
reserve f for VColoring of G;
reserve g for EColoring of G;
reserve t for TColoring of G;

theorem Th174:
  for G2 being edgeless _Graph, v,e,w being object
  for G1 being addAdjVertex of G2,v,e,w holds G1 is 3-tcolorable
proof
  let G2 be edgeless _Graph, v,e,w being object;
  let G1 be addAdjVertex of G2,v,e,w;
  G1 is 2-vcolorable 1-ecolorable by Th38;
  then G1 is (2+`1)-tcolorable by Th163;
  hence thesis;
end;
