Leticia Mattos:

Date: 2024-07-10

Time: 13:00 - 14:00

Zoom link: https://kva-se.zoom.us/j/9217561880

Leticia Mattos, Heidelberg University

We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense Erd\H os-Rényi random graph $G(n,p)$. Recently Acan and Kahn showed that the largest such family contains only $O(n^2/(\log{n})^3)$ cliques, with high probability, which disproved a conjecture of Alon and Spencer. We prove the corresponding lower bound, $\Omega(n^2/(\log{n})^3)$, by considering a random graph process which sequentially selects and deletes near-maximal cliques. To analise this process we use the Differential Equation Method. We also give a new proof of the upper bound $O(n^2/(\log{n})^3)$ and discuss the problem of the precise size of the largest such clique packing.