β Scribed by L.G. Bouma; W.T. Van Est
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We give necessary and sufficient conditions for a directed graph embedded on the torus or the Klein bottle to contain pairwise disjoint circuits, each of a given orientation and homotopy, and in a given order. For the Klein bottle, the theorem is new. For the torus, the theorem was proved before by
We show how to construct all the graphs that can be embedded on both the torus and the Klein bottle as their triangulations.
There are two main purposes of this article. First we show that every 3-connected graph embedded in the torus or the Klein bottle has a spanning planar subgraph which is 2-connected, and in fact has a slightly stronger connectivity property. Second, this subgraph is applied to show that every 3-conn
Closed-form expressions are obtained for the generating function of close-packed dimers on a 2 M = 2 N simple quartic lattice embedded on a Mobius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with those ΓΌnder cylindrical and free boundary conditions. Particularly,