I currently work for Pizza Hut. Pizza Hut is part of the Yum! corporation, encompassing Taco Bell, KFC, Long John Silvers, and something else, I think. At any rate, the mop handles they use are pretty much universally 7/8" hollow fiberglass, and they all have the same supplier AFAIK. When they break, only the very tip splits or splinters. They are a base length of 60", so needing to only cut ~3" off, you're still left with a little bit of a core left. At any rate, I got 5 of em from my work, and I thought, hey, I bet if anyone walked in off the street and asked the manager for any broken mop handles, I'm sure they would supply, as long as they were lying around. So yeah. Check out your local Yum! corporate "dining" institutions.
Note: They break because the mop head is held on by a little nub with a * through it, so that's the piece that breaks lose. It doesn't damage the structural integrity as a whole, just the bottom couple of inches.
Hope this helps someone score some free cores.
double-derp EDIT: They're actually 15/16" with an 1/16" wall