Large joints in graphs
We show that if r≥s≥2,n>r8, and G is a graph of order n containing as many r-cliques as the r-partite Turán graph of order n, then G has more than nr-1/r2r+12 cliques sharing a common edge unless G is isomorphic to the r-partite Turán graph of order n. This structural result generalizes a previous result that has been useful in extremal graph theory. © 2010 Elsevier Ltd.
European Journal of Combinatorics
Bollobás, B., & Nikiforov, V. (2011). Large joints in graphs. European Journal of Combinatorics, 32 (1), 33-44. https://doi.org/10.1016/j.ejc.2010.07.010