Re: Minimal Counter-example to the 4CT.


Proginoskes wrote:
bill wrote:
Proginoskes wrote:
Chip Eastham wrote:
[...]
I'm confused what you are asking. "Minimal counterexample"
has a pretty clearly defined in meaning with respect to 4CT,

Or in any other proof. A graph G is a minimal counterexample to a
proposition T if

(1) T is not true for G, and
(2) If H has fewer vertices than G, then T is true for H.

The idea is similar to that of "Infinite Descent".

Thr principle of "Infinite Descent" is a valid method of mathematical
proof. A summary is given in;.
http://mcraefamily.com/MathHelp/PythagInfiniteDescent.htm

Generally, ID says that you start with the assumption of minimality and
then find
something smaller.. But in the long run, it is not nrcessary to start
with an assumption of minimality.

It seems to me that ID is a viable way of proving that an "mce to the
4CT" does not exist. Could I be wrong?

Yes.

But am I wrong?

--- Christopher Heckman

.

Relevant Pages

  • Re: Minimal Counter-example to the 4CT.
    ... "Minimal counterexample" ... What you're doing is putting a total ordering on the planar graphs ... has clarified the meaning of "maximal" and the purpose ...
    (sci.math)
  • Re: Minimal Counter-example to the 4CT.
    ... Chip Eastham wrote: ... "Minimal counterexample" ... has a pretty clearly defined in meaning with respect to 4CT, ... --- Christopher Heckman ...
    (sci.math)
  • Re: Minimal Counter-example to the 4CT.
    ... "Minimal counterexample" ... has a pretty clearly defined in meaning with respect to 4CT, ... ordering to place on candidates (planar graphs here). ... This too could prove handy. ...
    (sci.math)
  • Re: Minimal Counter-example to the 4CT.
    ... Proginoskes wrote: ... "Minimal counterexample" ... has a pretty clearly defined in meaning with respect to 4CT, ... --- Christopher Heckman ...
    (sci.math)
  • Re: Minimal Counter-example to the 4CT.
    ... bill wrote: ... "Minimal counterexample" ... has a pretty clearly defined in meaning with respect to 4CT, ... --- Christopher Heckman ...
    (sci.math)
Quantcast