Definition 43: If a graph is planar, so will be any graph obtained by omitted an edge u, vl and adding a new vertex w together with edges u, w) and ww, vg. Such an operation is called an elementary subdivision Definition 44: The graphS G(VE1 and G2=(V2,E2)are called homeomorphic if they can be obtained from the same graph by a sequence of elementary subdivisions▪ Definition 43: If a graph is planar, so will be any graph obtained by omitted an edge {u,v} and adding a new vertex w together with edges {u,w} and {w,v}. Such an operation is called an elementary subdivision. ▪ Definition 44: The graphs G1=(V1 ,E1 ) and G2=(V2 ,E2 ) are called homeomorphic if they can be obtained from the same graph by a sequence of elementary subdivisions