The Tenth of Tevet is a fast day commemorating the beginning of the siege of Jerusalem which led to the destruction of the First Temple. It is therefore the first of the four fasts1 relating directly to the destruction of the Temple and Exile. Maimonides tells us that in the future, when the Temple is rebuilt, all these fasts will become times of festivity.
The fast of the Tenth of Tevet always occurs in proximity to the Shabbat on which the parshah of Vayigash (Genesis 44:18-47:27) is read. We can see a relationship between the fast and the events in our parshah.
From the time of Jacob's marriage to Rachel and Leah, there was conflict between the children of these two wives. Joseph, the son of Rachel, was sold into slavery by the children of Leah. Generations later, after the death of King Solomon, the Jewish people divided in two: the Southern Kingdom of Judah, the son of Leah, and the Northern Kingdom of Ephraim, grandson of Rachel.
The Prophets assure us that in the time of the Messiah there will at last be unity within the Jewish people. A foretaste of this is seen in the parshah, when Joseph reveals his identity to his brothers and they are reconciled. The theme of division and unity joins the parshah and the Fast of Tevet, which will soon become a joyous festival.2