Some NP-complete problems for hypergraph degree sequences

Charles J. Colbourn, W. L. Kocay, D. R. Stinson

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


A k-hypergraph G has vertex-set V(G) and edge-set E(G) consisting of k-subsets of V(G). If uε{lunate}V(G), then those edges of G containing u define a (k-1)-hypergraph Gu. We say G subsumes the (k-1)-hypergraphs {Gu|;uε{lunate}V(G)}. Given n graphs (i.e., 2-hyperegraphs) g1, g2, ... gn, is there a 3-hypergraph G such that the subsumed graphs Gi{succeeds or equal to}gi, for i=1, 2, ..., n? Given only the degree sequences of n graphs g1, g2, ..., gn, is there a 3-hypergraph G whose subsumed graphs G1, G2, ..., Gn have the same degree sequences? We consider 3-hypergraphs with and without repeated edges. We prove these problems NP-complete. We indicate their relation to some well-known problems. The corresponding problems for 2-hypergraphs have simple polynomial solutions.

Original languageEnglish (US)
Pages (from-to)239-254
Number of pages16
JournalDiscrete Applied Mathematics
Issue number3
StatePublished - Jul 1986
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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