  In this paper, we study the maximum degree in non-empty induced subgraphs of
the Kneser graph $KG(n,k)$. One of the main results asserts that, for $k>k_0$
and $n>64k^2$, whenever a non-empty subgraph has $m\ge k{n-2\choose k-2}$
vertices, its maximum degree is at least $\frac 12(1-\frac {k^2}n) m -
{n-2\choose k-2}\ge 0.49 m$. This bound is essentially best possible. One of
the intermediate steps is to obtain structural results on non-empty subgraphs
with small maximum degree.
