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The number of loopless planar maps

โœ Scribed by Edward A. Bender; Nicholas C. Wormald

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
124 KB
Volume
54
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We derive a simple formula for the number of rooted loopless planar maps with a given number of edges and a given valency of the root vertex.

๐Ÿ“œ SIMILAR VOLUMES

The Number of Loopless 4-Regular Maps on
The Number of Loopless 4-Regular Maps on the Projective Plane
โœ Han Ren; Yanpei Liu ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 175 KB

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.

Enumeration of 2 -connected Loopless 4 -
Enumeration of 2 -connected Loopless 4 -regular Maps on the Plane
โœ Han Ren; Yanpei Liu; Zhaoxiang Li ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 195 KB

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

The star-chromatic number of planar grap
The star-chromatic number of planar graphs
โœ Moser, David ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 127 KB ๐Ÿ‘ 2 views

The star-chromatic number of a graph, a parameter introduced by Vince, is a natural generalization of the chromatic number of a graph. Here we construct planar graphs with star-chromatic number r, where r is any rational number between 2 and 3, partially answering a question of Vince.