Boundary chromatic polynomial
| dc.creator | Jacobsen, Jesper Lykke | |
| dc.creator | Saleur, Hubert | |
| dc.date | 2008-03-18 | |
| dc.date.accessioned | 2026-07-07T12:17:45Z | |
| dc.date.available | 2026-07-07T12:17:45Z | |
| dc.description | We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Q_s colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition function of a boundary loop model. Using results for the latter, the phase diagram of the coloring problem (with real Q and Q_s) is inferred, in the limits of two-dimensional or quasi one-dimensional infinite graphs. We find in particular that the special role played by Beraha numbers Q=4 cos^2(pi/n) for the usual chromatic polynomial does not extend to the case Q different from Q_s. The agreement with (scarce) existing numerical results is perfect; further numerical checks are presented here. | |
| dc.description | 20 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/0803.2665 | |
| dc.identifier | http://arxiv.org/abs/0803.2665 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212180 | |
| dc.subject | Mathematical Physics | |
| dc.title | Boundary chromatic polynomial | |
| dc.type | text |