A note on Prüfer-like coding and counting forests of uniform hypertrees

Christian Lavault (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

This note presents an encoding and a decoding algorithms for a forest of (labelled) rooted uniform hypertrees and hypercycles in linear time, by using as few as $n - 2$ integers in the range $[1,n]$. It is a simple extension of the classical Pr\"{u}fer code for (labelled) rooted trees to an encoding for forests of (labelled) rooted uniform hypertrees and hypercycles, which allows to count them up according to their number of vertices, hyperedges and hypertrees. In passing, we also find Cayley's formula for the number of (labelled) rooted trees as well as its generalisation to the number of hypercycles found by Selivanov in the early 70's.

Mots clés: Hypergraph; Forest of (labelled rooted) hypertrees; Pr\"{u}fer code; Encoding-decoding; $b$-uniform; Enumeration.; Enumeration

Domaines: Mathématique discrète [cs.DM]

Christian Lavault. A note on Prüfer-like coding and counting forests of uniform hypertrees. 8th International Conference on Computer Science and Information Technologies (CSIT 2011), Sep 2011, Erevan, Armenia. pp.82-85. ⟨hal-00578191v3⟩