k-Pseudosnakes in n-dimensional Hypercubes

A k-pseudosnake in a graph is an induced subgraph of maximum degree at most k. In this paper we show that k-pseudosnakes with more than 2 n − 1 vertices exist in the hypercubes Q n , provided n ⩽ 2 k . We also give upper bounds, and show that the generated k-pseudosnakes are maximum provided k is even and n = 3 k / 2 . The results also yield better constructions of k-pseudosnakes in large n-dimensional grids in certain cases.