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

theorem Th43:
  for F being PGraphMapping of G1, G2
  st F is isomorphism holds G1 is c-vcolorable iff G2 is c-vcolorable
proof
  let F be PGraphMapping of G1, G2;
  assume A1: F is isomorphism;
  then reconsider F0 = F as one-to-one PGraphMapping of G1, G2;
  F0" is isomorphism by A1, GLIB_010:75;
  hence G1 is c-vcolorable implies G2 is c-vcolorable by Th42;
  thus G2 is c-vcolorable implies G1 is c-vcolorable by A1, Th42;
end;
