[Avodah] Asara B'Tevet

[Cantor Wolberg via Avodah]

I came across the following for what it is worth. It seems as if the geonim agrees with this being valid and a very 
good source is Yechezkel. Though it is obviously not followed in practice, it certainly exists in theory based on Yechezkel.

If a public fast falls on Shabbat, it is delayed until after Shabbat since fasting is not permitted on Shabbat. 
The one exception is Yom Kippur, which, based on a verse in the Torah, is observed even if it falls on Shabbat.  
Fascinatingly, the Geonim also write that the same was once true of the tenth of Tevet, since it is written of the tenth of Tevet: 
'On this very day' (YechezkeI 2). In our calendar calculation, however, the tenth of Tevet can never fall on Shabbat. 
One would wonder why the 10th of Tevet would've been observed on Shabbat, being a so-called minor fast day.  
The brilliant answer given is that since this day is the beginning of the whole chain of calamities, the beginning of anything 
is often times the most significant and determines the course and ultimate outcome.