Subgraphs with triangular components

Corradi and Hajnal [5] showed that if the minimum degree @d(G) of a graph on p vertices satisfies the inequality @d(G) >= 13(2@r - 1), then G has a subgraph consisting of [13@r] triangular components. They gave a class of graphs which shows that their inequality is best possible. In this paper, we characterize the extremal graphs G, and we thereby show that there are two classes of graphs G for which the inequality is best possible.