Question. Assume the truth of the (notoriously open) Evasiveness Conjecture. Does this constructively imply the negation of the Pizzazz-conjecture?
Remarks.
- The relevant statements are, by themselves, so natural, and transparently explained in the links given, that repeating them here seems superfluous. In particular, let
'Pizzazz-conjecture'$\equiv$'The graph-property $\mathcal{P}_{n,d}$ of all those graphs on $n$ which admit of a faithful orthogonal representation in $d$-dimensional Euclidean space is monotone-decreasing.'
The adverb 'constructively' in the question-statement is not precisely-defined. You may substitute it with 'reasonably' or 'appreciably'.
This question was motivated by an embarassing gaffe of mine in the thread cited above (a fallacious proof by contradiction of the negation of the Pizzazz-conjecture). It still seems to me that there should be
an easy argument why Pizzazz' $\mathcal{P}_{n,d}$ cannot possibly be monotone; assuming EC should strong be enough a tool to give a good argument.
- Needless to say, this is all about whether there is good argument why the property defined by Pizzazz cannot possibly be evasive. I.e., can one be always be sure to have a representable graph before the last edge has been uncovered?
