Re: Why Archimedes Plutonium will never proof the 4CT


Proginoskes wrote:
Gottfried Helms wrote:
Hi Christopher -

noting the effort, you've put into this discussion, I want
to add one remark, that at least to one reader you were able
to open eyes ;-)

Some years ago I had a similar discussion with some mathematician,
and I was in the position as AP: I could not understand, why
he denied my no-5-adjacent idea as a proof. Well, we had no
hassle about that, and I gave it a chance to possibly come out
to be understandable later. The current discussion solved that
inherent problem in my understanding. What I take now with me,
is that if the "non-5-adjacent"/"inside-triange-outside-triangle"
argument should be the core of the proof, then someone must prove
that any configuration can be reduced to a representation of
such (nested) non-5-adjacent-sub-configurations.
Is it that/something like, what A&H did with their computer-
proof?

It's like it. A&H's proof is direct, and they showed that there is a
fixed list of 1476 graphs such that: if you have a planar graph, then
it contains a graph on that list. (This is the "unavoidable
configuration" list.) AP's graphs do not form a list of unavoidable
configurations.

Every maximal planar graph contains a wheel graph of order six or less|
Is this graph one of the 1475 A&H graphs? If you initially consider
only maximal planar graphs; then you have only to consider the wheel
graph of order 6. The decsion to study only maximal planar graphs is
justified by the observation that any planar graphs can be maximalized
by the addition of a sufficient number of edges.

--- Christopher Heckman

Am 29.01.2006 07:05 schrieb Proginoskes:
Archimedes Plutonium [AP] has posted two alleged proofs of the 4CT
which are short but not correct. There are two basic facts that he is
repeatedly ignoring, and since the threads containing those proofs have
turned into many-headed hydrae, and since AP doesn't like reading long
posts, my points are lost. So I decided to start a new thread.


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