ON THE STRUCTURE OF LUCAS CUBES

Lucas cubes are induced subgraphs of hypercubes obtained by excluding from the hypercube's vertex set all binary strings with two consecutive ones, as well as with one in the first and the last position. They are closely related to Fibonacci cubes. It is well known, that a Lucas cube of order n consists of two Fibonacci cubes of order n - 1 and n - 3 with additional edges between them. We characterize Lucas cubes based on peripheral expansions of a unique convex subgraph of an appropriate Fibonacci cube. This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.