Paper Info
Title
The empire problem in even embeddings on closed surfaces with ε≤0ε≤0.
Abstract
Let M be a map on a closed surface F2 and suppose that each country of the map has at most r disjoint connected regions. Such a map is called an r-pire map on F2. In 1890, Heawood proved that the countries of M can be properly colored with ⌊(6r+1+(6r+1)2−24ε)/2⌋ colors, where ε is the Euler characteristic of F2. Also, he conjectured that this is best possible except for the case (ε,r)=(2,1), and now it is proved for all cases where ε≥0 and some cases where ε<0.
Year
DOI
Venue
2013
10.1016/j.disc.2012.10.024
Discrete Mathematics
Keywords
DocType
Volume
Empire problem,Even embedding,Current graph
Journal
313
Issue
ISSN
Citations 
19
0012-365X
0
PageRank 
References 
Authors
0.34
5
1
Name
Order
Citations
PageRank
Kenta Noguchi100.68