Equivalence between Hypergraph Convexities

Algorithm 1

(1) If |𝑋|≤1 then set 𝑌∶=𝑋 and Exit.

(2) Prune 𝑇 by repeatedly removing a leaf if

  (i) either it is a cutpoint-node

  (ii) or it is a block-node, say B, and

    either 𝑋∩𝑉(𝐵)=∅

    or |𝑋∩𝑉(𝐵)|=1 and the vertex in 𝑋∩𝑉(𝐵) is the cutpoint-node adjacent to B.

 Let 𝑇^ be the resultant tree.

(3) Set 𝑌∶=∅. For each block-node 𝐵 of 𝑇^, set 𝑌∶=𝑌⋃𝑉(𝐵).