Hybrid triple systems and cubic feedback sets

Charles J. Colbourn, William R. Pulleyblank, Alexander Rosa

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


A c-hybrid triple system of order v is a decomposition of the complete v-vertex digraph into c cyclic tournaments of order 3 and {Mathematical expression} transitive tournaments of order 3. Hybrid triple systems generalize directed triple systems (c = 0) and Mendelsohn triple systems (c = v(v - 1)/3); omitting directions yields an underlying twofold triple system. The spectrum of v and c for which a c-hybrid triple system of order v exists is completely determined in this paper. Using (cubic) block intersection graphs, we then show that every twofold triple system of order {Mathematical expression} underlies a c-hybrid triple system with {Mathematical expression}. Examples are constructed for all sufficiently large v, for which this maximum is at most {Mathematical expression}. The lower bound here is proved by establishing bounds on Fi(n, r), the size of minimum cardinality vertex feedback sets in n-vertex i-connected cubic multigraphs having r repeated edges. We establish that {Mathematical expression}, {Mathematical expression}. These bounds are all tight, and the latter is used to derive the lower bound in the design theoretic problem.

Original languageEnglish (US)
Pages (from-to)15-28
Number of pages14
JournalGraphs and Combinatorics
Issue number1
StatePublished - Dec 1989
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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