Maximal hypercubes in Fibonacci and Lucas cubes

Michel Mollard (1)

1 IF - Institut Fourier

The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1's. The Lucas cube $\Lambda_n$ is obtained from $\Gamma_n$ by removing vertices that start and end with 1. We characterize maximal induced hypercubes in $\Gamma_n$ and $\Lambda_n$ and deduce for any $p\leq n$ the number of maximal $p$-dimensional hypercubes in these graphs.

Mots clés: Hypercubes; cube polynomials; Fibonacci cubes; Lucas cubes

Domaines: Combinatoire [math.CO]

Michel Mollard. Maximal hypercubes in Fibonacci and Lucas cubes. 2012. ⟨hal-00657456⟩