In this paper rooted loopless (near) 4-regular maps on surfaces such as the sphere and the projective plane are counted and exact formulae with up to three or four parameters for such maps are given. Several classical results on regular maps and one-faced maps are deduced.
4-Regular Maps on the Klein Bottle
β Scribed by Han Ren; Yanpei Liu
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 245 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper rooted (near-) 4-regular maps on the plane are counted with respect to the root-valency, the number of edges, the number of inner faces, the number of non-root vertex loops, the number of non-root vertex blocks, and the number of multi-edges. As special cases, formulae of several types
## Abstract A (plane) 4βregular map __G__ is called __C__βsimple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case Ο (__G__) is the smallest integer __k__ such that the curves of __G__ can be colored with __k__ colors in such a way that no two curves
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
On p. 272 of the above article, paragraph # 3 is incomplete. It should read as the following: Hence to prove Proposition 4 it is enough to show that the edges of Q 4 can be colored with 4 colors in such a way that each square has one edge of each color. Such a coloring is displayed on the following
## Abstract We study intrinsic biharmonic maps on a fourβdimensional domain into a smooth, compact Riemannian manifold. We prove a partial regularity result without the assumption that the second derivatives are squareβintegrable. Β© 2005 Wiley Periodicals, Inc.