Linear recognition of generalized Fibonacci cubes Qh(111)

The generalized Fibonacci cube Qh(f) is the graph obtained from the h-cube Qh by removing all vertices that contain a given binary string f as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube Qh(111) is the set of all binary strings b1b2 . . . bh containing no three consecutive 1’s. We present a new characterization of the 3rd order generalized Fibonacci cubes based on their recursive structure. The characterization is the basis for an algorithm which recognizes these graphs in linear time.