The triangle-free process
| dc.creator | Bohman, Tom | |
| dc.date | 2008-06-26 | |
| dc.date.accessioned | 2026-07-07T09:46:57Z | |
| dc.date.available | 2026-07-07T09:46:57Z | |
| dc.description | Consider the following stochastic graph process. We begin with the empty graph on n vertices and add edges one at a time, where each edge is chosen uniformly at random from the collection of potential edges that do not form triangles when added to the graph. The process terminates at a maximal traingle-free graph. Here we analyze the triangle-free process, determining the likely order of magnitude of the number of edges in the final graph. As a corollary we show that the triangle-free process is very likely to produce a Ramsey R(3,t) graph; that is, our analysis of the triangle-free process gives a new proof of the lower bound on R(3,t) previously established by Jeong Han Kim. The techniques introduced extend to the K_4-free process thereby establishing a small improvement in the best known lower bound on the Ramsey number R(4,t). | |
| dc.description | 24 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/0806.4375 | |
| dc.identifier | http://arxiv.org/abs/0806.4375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163705 | |
| dc.subject | Combinatorics | |
| dc.title | The triangle-free process | |
| dc.type | text |