It is indeed the सम्बन्ध; it's not a कारक technically. The canonical defn. of कारक is that which relates a noun to the verb. सम्बन्ध relates relations between nouns (you can't have sentences with only a verb and a noun in genitive).
It's not my concern if certain folk have no education in Panini, and are arrogant enough to ignore his work.