quasi
Posts:
12,021
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 4colored. >> >> >> >> With the definition as you've stated it, there's no such >> >> thing as a forced 5set. >> > >> >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 >> >4coloring 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 5set 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

