At Gil Kalai's blog, Hall’s theorem for hypergraphs (Ron Aharoni and Penny Haxell, 1999) is given, and then it says, "Ron Aharoni and Penny Haxell described special type of triangulations, and then miraculously deduced their theorem from Sperner’s lemma. This also gives a beautiful, completely new, topological proof of Hall’s marriage theorem itself."

At Gil Kalai's blog, Hall’s theorem for hypergraphs (Ron Aharoni and Penny Haxell, 1999) is given, and then it says, "Ron Aharoni and Penny Haxell described special type of triangulations, and then miraculously deduced their theorem from Sperner’s lemma. This also gives a beautiful, completely new, topological proof of Hall’s marriage theorem itself."

The Aharoni-Haxell paper is available here.