Geodesic
Covering small subgraphs of (hyper)tournaments with spanning acyclic subgraphs
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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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.
DOI : 10.37236/9336
Classification : 05C70, 05C20, 05C35
Mots-clés : \(k\)-tournament 
@article{10_37236_9336,
     author = {Raphael Yuster},
     title = {Covering small subgraphs of (hyper)tournaments with spanning acyclic subgraphs},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9336},
     zbl = {1450.05071},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9336/}
}
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Raphael Yuster. Covering small subgraphs of (hyper)tournaments with spanning acyclic subgraphs. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9336

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