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The Number of Loopless 4-Regular Maps on the Projective Plane

✍ Scribed by Han Ren; Yanpei Liu

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 175 KB
Volume: 84
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2064

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✦ Synopsis

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.

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## Abstract A (plane) 4‐regular map __G__ is called __C__‐simple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case σ (__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