Joints in graphs


In 1969 Erdo{combining double acute accent}s proved that if r ≥ 2 and n > n0 (r), every graph G of order n and e (G) > tr (n) has an edge that is contained in at least nr - 1 / (10 r)6 r cliques of order (r + 1). In this note we improve this bound to nr - 1 / rr + 5. We also prove a corresponding stability result. © 2007 Elsevier B.V. All rights reserved.

Publication Title

Discrete Mathematics