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;

theorem Th105:
  for G1 being addVertices of G2, V
  holds G1 is c-ecolorable iff G2 is c-ecolorable
proof
  let G1 be addVertices of G2, V;
  G2 is Subgraph of G1 by GLIB_006:57;
  hence G1 is c-ecolorable implies G2 is c-ecolorable;
  assume G2 is c-ecolorable;
  then consider g2 being proper EColoring of G2 such that
    A1: card rng g2 c= c;
  the_Edges_of G1 = the_Edges_of G2 by GLIB_006:def 10;
  then reconsider g1 = g2 as EColoring of G1;
  g1 is proper by Th92;
  hence thesis by A1;
end;
