Efficient prüfer-like coding and counting labelled hypertrees

Abstract

We show that r-uniform hypertrees can be encoded in linear time using as little as n-2 integers in the range [1,n]. The decoding algorithm also runs in linear time. For general hypertrees, we require codes of length n+e-2, where e is the number of hyperedges. We show that there are at most distinct labeled r-uniform hypertrees, where f(n,r) is a lower bound on the number of trees with vertex degrees exceeding . We suggest a counting scheme for determining f(n,r).© 2006 Springer-Verlag Berlin/Heidelberg.