  For fixed $k$, we consider the subgraph $YF_k=(V_k,E_k)$ of the famous
Young--Fibonacci graph formed by the words with at most $k$ 2-s. The jump graph
is a graded graph is defined as follows: each level is identified with $V_k$,
and an edge between two vertices $(v_1,i)$ and $(v_{2},i+1)$, $v_1,v_2\in V_k$,
of neighbouring levels us drawn iff $v_2$ is a descendant of $v_1$ in $YF_k$.
The goal of this paper is to describe all central measures on the path space of
$YF_k$.
