  For integers $k\geq 1$ and $n\geq 2k+1$ the Kneser graph $K(n,k)$ has as
vertices all $k$-element subsets of $[n]:=\{1,2,\ldots,n\}$ and an edge between
any two vertices (=sets) that are disjoint. The bipartite Kneser graph $H(n,k)$
has as vertices all $k$-element and $(n-k)$-element subsets of $[n]$ and an
edge between any two vertices where one is a subset of the other. It has long
been conjectured that all Kneser graphs and bipartite Kneser graphs except the
Petersen graph $K(5,2)$ have a Hamilton cycle. The main contribution of this
paper is proving this conjecture for bipartite Kneser graphs $H(n,k)$. We also
establish the existence of cycles that visit almost all vertices in Kneser
graphs $K(n,k)$ when $n=2k+o(k)$, generalizing and improving upon previous
results on this problem.
