[kayodelycaon]

Sabers? Katanas?

[rascul]

Also falchions, scimitars, sabres, cutlasses, and falcatas. Additionally, I have some double edged knives.

[randomswede]

For sabres, I'd say "it depends". A non-trivial fraction will have a portion of the back sharpened (about a quarter to a third).

But, yes, there are more definitely single-edged swords. Add falchion to the list (or a langmesser, although that literally means "long knife").

I guess it is genuinely hard to draw a non-fuzzy line between "knife" and "sword"...