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Topic: A New Graph Coloring Conjecture.
Replies: 42   Last Post: Jul 2, 2013 4:08 AM

 Messages: [ Previous | Next ]
 b92057@yahoo.com Posts: 1,187 Registered: 4/18/05
Re: A New Graph Coloring Conjecture.
Posted: Jun 27, 2013 12:10 AM

On Wednesday, June 26, 2013 12:49:42 AM UTC-7, quasi wrote:
> Bill wrote:
>
>
>

> >I took a second look at your graph information. When I say
>
> >those virtually invisible dots, I had enough to analyze the
>
> >graoh for FFS. I found one. It is vetices 1 7 8 9. Not a K4.
>
>
>
> Right, the subgraph determined by vertices 1,7,8,9 is not a
>
> K4, but it's not what you call a forced 4-set, since it's
>
> 3-colorable.
>
>
>
> As I previously noted, if a graph with 4 vertices is not
>
> 3-colorable, then it must be complete (that is, it must be
>
> isomorphic to K4).
>
>
>
> quasi

1 4 4 7
7 . 2 4 5 7
|\ . 2 5 6 7
= 3 . | \ 8 3 4 8 5
| . | \ ./| 3 5 8 6
| 0 . \/ | 3 6 9 4
| . | . \ | 4 5
| . | /.\| 4 6
2-------|--/---9 5 6
. | / .
. |/ .
1
ANALYSIS;

1. Arbitrarily assign colors initial
colors; 4=B 5=C 6=D

2. This forces 3=A & 7=A.

3. 8=B is forced by 7=A 5=C & 6=D

4. 9-C is forced by 6=D, 7=A & 8=B

5. 1=D is forced by 7=A, 8=B & 9=C

A classic example of what I call a "forced
four subset".

bill

Date Subject Author
6/18/13 b92057@yahoo.com
6/18/13 Tucsondrew@me.com
6/18/13 Tucsondrew@me.com
6/18/13 quasi
6/18/13 Tucsondrew@me.com
6/18/13 quasi
6/19/13 trj
6/20/13 b92057@yahoo.com
6/20/13 quasi
6/20/13 b92057@yahoo.com
6/22/13 b92057@yahoo.com
6/23/13 quasi
6/25/13 b92057@yahoo.com
6/25/13 quasi
6/25/13 b92057@yahoo.com
6/26/13 quasi
6/26/13 Brian Q. Hutchings
6/27/13 b92057@yahoo.com
6/27/13 quasi
6/27/13 b92057@yahoo.com
6/27/13 quasi
6/27/13 quasi
6/28/13 b92057@yahoo.com
6/28/13 quasi
6/28/13 b92057@yahoo.com
6/29/13 quasi
7/1/13 b92057@yahoo.com
7/2/13 quasi
6/19/13 b92057@yahoo.com
6/19/13 quasi
6/20/13 b92057@yahoo.com
6/20/13 Tucsondrew@me.com
6/21/13 quasi
6/21/13 quasi
6/22/13 b92057@yahoo.com
6/23/13 quasi
6/19/13 b92057@yahoo.com
6/20/13 quasi
6/20/13 quasi
6/20/13 Butch Malahide
6/20/13 Butch Malahide
6/19/13 b92057@yahoo.com
6/20/13 b92057@yahoo.com