Large -tilings and Hamilton -cycles in -uniform hypergraphs

For (Figure presented.), let (Figure presented.) be the (Figure presented.) -uniform hypergraph with two edges intersecting in (Figure presented.) vertices. Our main result is that any (Figure presented.) -vertex 3-uniform hypergraph with at least (Figure presented.) edges contains a collection of (Figure presented.) vertex-disjoint copies of (Figure presented.), for (Figure presented.). The bound on the number of edges is asymptotically best possible. This problem generalizes the Matching Conjecture of Erdős. We then use this result combined with the absorbing method to determine the asymptotically best possible minimum (Figure presented.) -degree threshold for (Figure presented.) -Hamiltonicity in (Figure presented.) -graphs, where (Figure presented.) is odd and (Figure presented.). Moreover, we give related results on (Figure presented.) -tilings and Hamilton (Figure presented.) -cycles with (Figure presented.) -degree for some other values of (Figure presented.).