Clique packings in random graphs
| Autor: | Griffiths, Simon, Mattos, Letícia |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense Erd\H{o}s-R\'enyi 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 analyse 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. Comment: 43 pages |
| Databáze: | arXiv |
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