Determining the L(2, 1)-span in polynomial space

An $L(2,1)$-labeling of a graph is a labeling of its vertices by nonnegative integers, such that the labels of adjacent vertices differ by at least $2$ and labels assigned to vertices with a common neighbor differ by at least $1$. The span of a labeling is the difference of the smallest and largest labels used. It is known that finding a minimum span of any given graph is NP-Complete. In this paper we present an algorithm for this problem, which works in time $O(7.9463^n)$ and uses only polynomial memory. This is the first exact algorithm for $L(2,1)$-labeling problem with time complexity $O(c^n)$ for some constant $c$ and polynomial space complexity