ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
| Hi-index | 0.01 |
This paper concludes the characterization of 3-realizable graphs begun by Belk and Connelly. A graph is 3-realizable if, for every configuration of its vertices in EN with N ≥ 3, there exists a corresponding configuration in E3 with the same edge lengths. In this paper the two graphs V8 and C5 × C2 are shown to be 3-realizable. As shown by Belk and Connelly, this means that the forbidden minors for 3-realizability are K5 and K2,2,2.A graph is d-realizable if, for every configuration of its vertices in EN, there exists a another corresponding configuration in Ed with the same edge lengths.