International Scholarly Research Notices / 2011 / Article / Alg 1

Research Article

Equivalence between Hypergraph Convexities

Algorithm 1

(1) If | 𝑋 | ≀ 1 then set π‘Œ ∢ = 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 ( 𝐡 ) = βˆ…
    or | 𝑋 ∩ 𝑉 ( 𝐡 ) | = 1 and the vertex in 𝑋 ∩ 𝑉 ( 𝐡 ) is the cutpoint-node adjacent to B.
 Let 𝑇 ξ…ž be the resultant tree.
(3) Set π‘Œ ∢ = βˆ… . For each block-node 𝐡 of 𝑇 ξ…ž , set ⋃ π‘Œ ∢ = π‘Œ 𝑉 ( 𝐡 ) .

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