Sudden emergence of q-regular subgraphs in random graphs
| dc.creator | Pretti, Marco | |
| dc.creator | Weigt, Martin | |
| dc.date | 2006-03-30 | |
| dc.date.accessioned | 2026-07-07T07:05:06Z | |
| dc.date.available | 2026-07-07T07:05:06Z | |
| dc.description | We investigate the computationally hard problem whether a random graph of finite average vertex degree has an extensively large $q$-regular subgraph, i.e., a subgraph with all vertices having degree equal to $q$. We reformulate this problem as a constraint-satisfaction problem, and solve it using the cavity method of statistical physics at zero temperature. For $q=3$, we find that the first large $q$-regular subgraphs appear discontinuously at an average vertex degree $c_\reg{3} \simeq 3.3546$ and contain immediately about 24% of all vertices in the graph. This transition is extremely close to (but different from) the well-known 3-core percolation point $c_\cor{3} \simeq 3.3509$. For $q>3$, the $q$-regular subgraph percolation threshold is found to coincide with that of the $q$-core. | |
| dc.description | 7 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0603819 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0603819 | |
| dc.identifier | Europhys. Lett. 75, 8 (2006) | |
| dc.identifier | doi:10.1209/epl/i2006-10070-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109562 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Sudden emergence of q-regular subgraphs in random graphs | |
| dc.type | text |