We give a minimal change list for the set of order p length-n Lucas strings, i.e., the set of length-n binary strings with no p consecutive 1's nor a 1l prefix and a 1m suffix with l+m ≥ p. The construction of this list proves also that the order p n-dimensional Lucas cube has a Hamiltonian path if and only if n is not a multiple of p + 1, and its second power always has a Hamiltonian path.
['Jean-Luc Baril', 'Vincent Vajnovszki']
Minimal change list for Lucas strings and some graph theoretic consequences