Geodesic
Lichiardopol's conjecture on disjoint cycles in tournaments
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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In 2010, Lichiardopol conjectured for $q \geqslant 3$ and $k \geqslant 1$ that any tournament with minimum out-degree at least $(q-1)k-1$ contains $k$ disjoint cycles of length $q$. Previously the conjecture was known to hold for $q\leqslant 4$. We prove that it holds for $q \geqslant 5$, thereby completing the proof of the conjecture.
DOI : 10.37236/7715
Classification : 05C20, 05C70, 05C38, 05C12, 05C07
Mots-clés : minimum outdegree, disjoint 3-cycles 
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     author = {Fuhong Ma and Douglas B. West and Jin Yan},
     title = {Lichiardopol's conjecture on disjoint cycles in tournaments},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/7715},
     zbl = {1441.05093},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7715/}
}
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Fuhong Ma; Douglas B. West; Jin Yan. Lichiardopol's conjecture on disjoint cycles in tournaments. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/7715

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