(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2003)
Let G be a graph, χ(G)=r and cl(G) < r. Dirac has proved in [2] that for such graph |V(G)|r+2 and |V(G)| = r+2 only if G=K_r-3+C_5. The main result in the current article generalizes the proposition mentioned above (Theorem 2.1). As a consequence of Theorem 2.1, some results for Folkman graphs are obtained (Theorems 7.1–7.4, 8.1).