Name
Abstract | ||
|---|---|---|
Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this work we show that it is NP-complete to decide whether or not a surface triangulation admits a satisfying spin-assignment, and that it is #P-complete to determine the number of such assignments. Both results are derived via an elaborate (and atypical) reduction that maps a Boolean formula in 3-conjunctive normal form into a triangulation of an orientable closed surface. |
Year | Venue | Keywords |
|---|---|---|
2011 | CoRR | computational complexity,conjunctive normal form,satisfiability,ising model |
Field | DocType | Volume |
Discrete mathematics,Graph,Spin-½,Combinatorics,Surface triangulation,Ising model,Duality (optimization),Triangulation (social science),True quantified Boolean formula,Mathematics,Antiferromagnetism | Journal | abs/1107.3767 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrea Jiménez | 1 | 8 | 4.13 |
| Marcos A. Kiwi | 2 | 169 | 24.15 |