AN INDUCTIVE CONSTRUCTION OF (2,1)-TIGHT GRAPHS

The graphs G = (V, E) with vertical bar E vertical bar = 2 vertical bar V vertical bar - l that satisfy < vertical bar E'vertical bar = 2 vertical bar V'vertical bar - l for any subgraph G' - (V', E') (and for l - 1, 2, 3) are the (2,l)-tight graphs. The Henneberg-Laman theorem characterizes (2, 3)-tight graphs inductively in terms of two simple moves, known as the Henneberg moves. Recently, this has been extended, via the addition of a graph extension move, to the case of (2, 2)-tight simple graphs. Here an alternative characterization is provided by means of vertex-to-K-4 and edge-to-K-3 moves. This is extended to the (2, 1)-tight simple graphs by the addition of an edge joining move.