Joints in graphs

In 1969 Erdos proved that if r>=2 and n>n"0(r), every graph G of order n and e(G)>t"r(n) has an edge that is contained in at least n^r^-^1/(10r)^6^r cliques of order (r+1). In this note we improve this bound to n^r^-^1/r^r^+^5. We also prove a corresponding stability result.