 About 9,830 results  books.google.com If m equals 1 (that is, if each country consists of only one region), the problem is
equivalent to the fourcolor problem, and ... In other words, the solution to the m
pire problem for the case m = 2 was obtained long before the solution for the
case ... 

 books.google.com I'm going to grab some of your things and take you out of this house” “Why are
you here?” “Once you left the house, the cravings started to hit me last ... You don'
t think you have a problem.” “Yes, I have a problem. I'm being haunted.” “That is ... 

 books.google.com “That's part of the game. ..and the problem. I don't know how to get his ... “At least
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 books.google.com For the four planet problem, k 4 is either 22, 23, or 24. For the m planet problem, k
,l is either 6m—2, 6m—1, or 6m. The proof of the upper bound is the same as that
for the mpire problem, and for the lower bound, the thickness of the complete ... 

 books.google.com The "Four Color Problem" was born: Are four colors sufficient for every possible
map? (It is understood that ... See Ian Stewart's article The Rise and Fall of the
Lunar Mpire in the April 1993 issue of the Scientific American. We have
formulated ... 

 books.google.com Percy Heawood (1890) studied the coloring problem for the case when each
country consists of m disjoint regions. This is called the empire, or mpire,
problem. He showed that 6m colors are sufficient in this more general case and
that, for m ... 

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will help you resolve it stepbystep. ... He recently served on the customer
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 books.google.com The problem is set on the Earth only, but now each country is part of an empire
containing a maximum of m countries, and the same colour must be used ...
Heawood proved that an mpire can always be coloured with 6m colours, for all
m 2 2. 

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 books.google.com If each empire consists of exactly m regions, this is called the 'mpire' problem.
The usual mapcolouring problem is thus the 1 pire problem . For example , in
the 2pire problem , we consider all maps in which different regions are
associated ... 

 