Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
quasi

Posts: 10,305
Registered: 7/15/05
Re: A New Graph Coloring Conjecture.
Posted: Jun 29, 2013 3:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

>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
Read A New Graph Coloring Conjecture.
b92057@yahoo.com
6/18/13
Read Re: A New Graph Coloring Conjecture.
Tucsondrew@me.com
6/18/13
Read Re: A New Graph Coloring Conjecture.
Tucsondrew@me.com
6/18/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/18/13
Read Re: A New Graph Coloring Conjecture.
Tucsondrew@me.com
6/18/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/19/13
Read Re: A New Graph Coloring Conjecture.
trj
6/20/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/20/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/20/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/22/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/23/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/25/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/25/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/25/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/26/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/26/13
Read Re: A New Graph Coloring Conjecture.
Brian Q. Hutchings
6/27/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/27/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/27/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/27/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/27/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/28/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/28/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/28/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/29/13
Read Re: A New Graph Coloring Conjecture.
quasi
7/1/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
7/2/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/19/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/19/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/20/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/20/13
Read Re: A New Graph Coloring Conjecture.
Tucsondrew@me.com
6/21/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/21/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/22/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/23/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/19/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/20/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/20/13
Read Re: A New Graph Coloring Conjecture.
quasi
6/20/13
Read Re: A New Graph Coloring Conjecture.
Butch Malahide
6/20/13
Read Re: A New Graph Coloring Conjecture.
Butch Malahide
6/19/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com
6/20/13
Read Re: A New Graph Coloring Conjecture.
b92057@yahoo.com

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.