• from the Wikipedia page of his nephew, Kayqubad I:

When the sultan died following the battle of Alaşehir in 1211,[1] both Kayqubad and his elder brother Kaykaus struggled for the throne. Kayqubad initially garnered some support among the neighbors of the sultanate: Leo I, the king of Cilician Armenia and Tughrilshah, the brothers' uncle and the independent ruler of Erzurum.

• from the Wikipedia page of his son, Ghias ad-Din:

The consort of Queen Rusudan was a younger son of 'Abdu'l Harij Muhammad Mughis ad-din Tughril Shah, the Seljuq emir of Erzurum, and his wife, a daughter of Sayf al-Din Begtimur, the ruler of Ahlat.[1] Tughril Shah had received Elbistan in appanage upon the division of the sultanate of Rum by his father Kilij Arslan II in 1192, but he exchanged it, c. 1201, for Erzurum.[2] He appears to have been a tributary to Georgia for at least parts of his reign.[3]

References

1. Djaparidze, Georgia and the Near Eastern Islamic world in the 12th–13th century, 1995, pp. 181–182.
2. Toumanoff, The Fifteenth-Century Bagratids and the Institution of Collegial Sovereignty in Georgia, 1949–1951, p. 181.
3. Peacock, Georgia and the Anatolian Turks in the 12th and 13th centuries, 2006, p. 130.