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 Th121:
  G is edgeless iff G.eChromaticNum() = 0
proof
  hereby
    assume G is edgeless;
    then G.size() = 0;
    hence G.eChromaticNum() = 0 by Th120, XBOOLE_1:3;
  end;
  assume G.eChromaticNum() = 0;
  then G is 0-ecolorable by Lm14;
  hence thesis;
end;
