problem
- To: mathgroup at smc.vnet.net
- Subject: [mg27542] problem
- From: roeen yaghobey <roeeny at yahoo.com>
- Date: Sat, 3 Mar 2001 03:40:27 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Would you help me to prove or counterexample a problem
in this book " Discrete and combinatorial Mathematics
, an Applied introduction , by : Ralph P. Grimaldi ,
second edition, Addison-Wesley publishing co. , 1989 (
chapter 11 , example 11.7 )" , that I extended (for
n>=3 ) it ? as follow :
? We supposed that there are n - cubes & m - colors (
for n >= 3 ) so m=n . The Graph of G that m-colors is
vertices and the opposit faces of cubes are their
edges . ( The number of edges = 3n )
If there are the subgraphs of G1 & G2 that their
vertices are degree 2 . ( deg(vi) = 2 ) They have two
specifications : ( G1 & G2 have n - vertices )
1 - In G1 , we supposed for every color , there is a
loop and none of the two colors are connected to each
other .
2 - In G2 , there is a cycle with n - length & it is
connected .
Then , when we placed these n-cubes altogether from 4
- sides , m - colors are defined .
Sincerely yours ,
Roeen Yaghouby ,
Student pre-college , I.R.
Roeeny@ yahoo.com
Address: R.yaghouby ,14th Eastern st. ,Ajdanie
st. ,Niavaran st. ,No.19 ,Tehran ,Iran , Post No. :
1956816894
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