Given n subsets of cardinality k of a set $S=\{1,2,...,m\}$. Is there a polynomial time algorithm to determine if there exists an ordering of subsets $s_1,...,s_n$ such that $|s_i\backslash\bigcup_{j<i}s_j|=1$ for $i=2,...,n$?
Note: In my ongoing research, $k=4$ and $m=n+3$.