تقرير
On the triangle space of a random graph
| العنوان: | On the triangle space of a random graph |
|---|---|
| المؤلفون: | DeMarco, Bobby, Hamm, Arran, Kahn, Jeff |
| سنة النشر: | 2012 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Combinatorics, 05C80, 05C35, 05D40, 55U10, 60C05 |
| الوصف: | Settling a first case of a conjecture of M. Kahle on the homology of the clique complex of the random graph $G=G_{n,p}$, we show, roughly speaking, that (with high probability) the triangles of $G$ span its cycle space whenever each of its edges lies in a triangle (which happens (w.h.p.) when $p$ is at least about $\sqrt{(3/2)\ln n/n}$, and not below this unless $p$ is very small.) We give two related proofs of this statement, together with a relatively simple proof of a fundamental "stability" theorem for triangle-free subgraphs of $G_{n,p}$, originally due to Kohayakawa, \L uczak and R\"odl, that underlies the first of our proofs. Comment: 20 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1207.6717 |
| رقم الأكسشن: | edsarx.1207.6717 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |