System Information
Operating system and graphics card

Blender Version
Broken:2.74 hash:000dfc0

Short description of error

When using 'Skin Resize' (ctrl-a) in edit mode on these edges (with the skin modifier applied), I get a 100% repeatable crash when it reaches 0. This is true for scaling with incremental snapping (the only way I could get to 0 manually), but I found out about it by typing in an exact size (0.3, so it first scales to zero).
Things I tried to fix this:
Changing the root vertex - did not change anything, it still crashed.
'Remove Doubles' - no doubles removed, still crashed
'Smooth' - Smoothed untill it was entirely smooth and untangled, still crashed.

'Select All', 'Checker Deselect', 'Dissolve Vertices'. - this fixed the problem, but I don't have the time to test vertex by vertex which one's the culprit.

Exact steps for others to reproduce the error
Select one of the meshes
Go into edit mode
'Select All' (a)
'Skin Resize' (ctrl-a)
Type in zero. This will crash to desktop immediately, without warning.

This is a pretty messy mesh, and undoubtable an edge case as far as what people use the Skin Modifier for, but it's 100% repeatable, and I've attached the .blend.

to hopefully narrow down what's happening.