In this lecture, I will give an edge condition for the existence of a Y_{k,b}-tiling with a fixed size which leads to some new results on d-degree Hamilton \ell-cycle problem. For all k≥3, 1≤\ell<k/2 and max{k-\ell,\ell+1} ≤d≤k-1, I will give an asymptotic bound on the minimum d-degree for the existence of Hamilton \ell -cycles in k-graphs, where k-\ell divides n. This asymptotic bound is the best possible for some cases.