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

 Messages: [ Previous | Next ]
 quasi Posts: 12,067 Registered: 7/15/05
Re: A New Graph Coloring Conjecture.
Posted: Jun 29, 2013 3:24 AM

>quasi wrote:
>> bill wrote:
>> >quasi wrote:
>> >> bill wrote:
>> >> >
>> >> >Forced Five Set: A connected subset of five vertices
>> >> >(not isomorphic to K5), that cannot be 4-colored.

>> >>
>> >> With the definition as you've stated it, there's no such
>> >> thing as a forced 5-set.

>> >
>> >Am I the only person who would like to see a short
>> >snappy proof of the 4 CT?

>>
>> Sure, that would be nice.
>>

>> >I hope to create a simple proof of the Four Color Theorem.
>> >In this context, I don't think that I will be allowed to
>> >presume that forced sets do not exist.

>>
>> But you _will_ be expected to give a rigorous mathematical
>> definition of forced sets. You previously said you couldn't
>> do that.

>
>Give me the mathematical definition of an impasse and
>I will try to adopt it to include forced sets.

>> >
>> >I m fairly certain that a forced set may be cited as
>> >the primary reason for the more common impasses.
>> >
>> >In this context; an unresolved impasse in the attempted
>> >4-coloring of a planar graph might be due to the presence
>> >of a forced set.

>>
>> If you can't define forced sets in a way that others can
>> understand, there's not much chance that anyone would be
>> able to follow a proposed proof of yours of the 4CT.

>
>Can you accept this definition?
>
>Consider;
>
>Impasse. A difficulty encountered in the attempted
> four coloring of a graph.
>
>Type I " An impasse that is created by the presence of a
>vertex adjacent to four other vertices, each of which has an
>assigned color that is different from the assigned color any
> of the three other vertices".
>
>Type II "All other impasses."

No, I don't view that as an acceptable definition.

It appears your concept of a forced 5-set in a graph G is a
set of 5 vertices, S = {a,b,c,d,e} say, such that

(1) Not all vertices of S are adjacent.

(2) One of the vertices of S, e say, is adjacent to the other 4.

(3) Vertices a,b,c,d have already somehow been forced to have
4 distinct colors.

My objection is to property (3). It's not clear what it means.

quasi

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