theorem :: GLCOLO00:173

for G2 being _Graph
for c being Cardinal
for v being Vertex of G2
for e, w being object
for G1 being addAdjVertex of G2,v,e,w st not e in the_Edges_of G2 & not w in the_Vertices_of G2 & v is endvertex & G2 is c -tcolorable holds
G1 is c -tcolorable