[Fictionary] SCROOP Definitions--Josh wins in a landslide

[Pierre Abbat]

> PIERRE
> 
> scroop - n. - (Mathematics) A graph in which every two distinct points have
> exactly one adjacent point in common and there is a cycle of length 5.
> 
> 0 POINTS
> 
> Jean-Joseph Comment: I thought about this a little, and I'm not sure if it's
> possible.  But it might be.  Anyone want to post an example?
> 
> Nicolas Comment: Isn't this just a pentagon? Although I wouldn't put it past
> mathematicians to have a special word.

There is no such graph. Once I took a graph theory course, and at the 
beginning the teacher told us to prove this proposition: If every two people 
have exactly one acquaintance in common, then there is someone who knows 
everybody. (This is not counting γνωθι σεαυτον, of course.) I reasoned: there 
cannot be a cycle of length 4 (which I called a devil), and if there is a 
cycle of length greater than 5, then there must be a cycle of length 5. I 
somehow managed to prove that a cycle of length 5 implies one of length 4, but 
I don't remember how. So there cannot be cycles of length greater than 3, and 
it's easy to see that all cycles of length 3 share a common point, which is 
the person who knows everybody.

A snark is a certain kind of cubic graph (a graph all of whose points have 
three edges). A planar snark is called a boojum. There is no boojum (the 
nonexistence of boojums is equivalent to the four-color theorem). I figured 
"scroop" could be a mathematical term of the same sort.

Pierre
-- 
The Black Garden on the Mountain is not on the Black Mountain.