Covering small subgraphs of (Hyper)tournaments with spanning acyclic subgraphs

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Abstract

While the edges of every tournament can be covered with two spanning acyclic subgraphs, this is not so if we set out to cover all acyclic H-subgraphs of a tournament with spanning acyclic subgraphs, even for very simple H such as the 2-edge directed path or the 2-edge out-star. We prove new bounds for the minimum number of elements in such coverings and for some H our bounds determine the exact order of magnitude. A k-tournament is an orientation of the complete k-graph, where each k-set is given a total order (so tournaments are 2-tournaments). As opposed to tournaments, already covering the edges of a 3-tournament with the minimum number of spanning acyclic subhypergraphs is a nontrivial problem. We prove a new lower bound for this problem which asymptotically matches the known lower bound of covering all ordered triples of a set.

Original languageEnglish
Article numberP4.13
Pages (from-to)1-15
Number of pages15
JournalElectronic Journal of Combinatorics
Volume27
Issue number4
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
∗Supported by Israel Science Foundation (grant No. 1082/16).

Publisher Copyright:
© The author. Released under the CC BY-ND license (International 4.0).

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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