On The Number Of Cliques In Graphs

Let krn(G) be the number of edge disj oint r-cliques in a graph G.Paul Erdos conjectured that k3n(G)≥m for all K4-free graphs G of order n size|(n2)/4|+m.In tnis paper we show tnat when G is a K4-free graph with n vertices and|(n2)+/4|+m edges,then k3n(G)≥?(32)/(35)m+o(n2).Moreover,if m≥(1+(?))/(88)n2,then k3n(G)≥m+o(n2).