A polynomial delay algorithm for generating connected induced subgraphs of a given cardinality

We give a polynomial delay algorithm, that for any graph G and positive integer k, enumerates all connected induced subgraphs of G of order k. Our algorithm enumerates each subgraph in at most O((k min{(n−k); k△})²(△+log k)) and uses linear space O(n+m), where n and m are respectively the number of vertices and edges of G and △ is the maximum degree.