Covering Small Subgraphs of (Hyper)Tournaments with Spanning Acyclic Subgraphs
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Published:2020-10-16
Issue:4
Volume:27
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
1 articles.
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