Department of

January 2020 February 2020 March 2020 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 1 2 3 4 5 6 7 5 6 7 8 9 10 11 2 3 4 5 6 7 8 8 9 10 11 12 13 14 12 13 14 15 16 17 18 9 10 11 12 13 14 15 15 16 17 18 19 20 21 19 20 21 22 23 24 25 16 17 18 19 20 21 22 22 23 24 25 26 27 28 26 27 28 29 30 31 23 24 25 26 27 28 29 29 30 31

Tuesday, January 21, 2020

**Abstract:** In a 1981 survey on cycles in digraphs, Bermond and Thomassen conjectured that every digraph with minimum outdegree at least $2k-1$ contains $k$ disjoint cycles. In 2010, Lichiardopol conjectured a stronger property for tournaments: for positive integers $k$ and $q$ with $q\ge3$, every tournament with minimum out-degree at least $(q-1)k-1$ contains $k$ disjoint cycles of length $q$.

Bang-Jensen, Bessy, and Thomassé [2014] proved the special case of the Bermond--Thomassen Conjecture for tournaments. This implies the case $q=3$ of Lichiardopol's Conjecture. The case $q=4$ was proved in a masters thesis by S. Zhu [2019]. We give a uniform proof for $q\ge5$, thus completing the proof of Lichiardopol's Conjecture. This result is joint work with Fuhong Ma and Jin Yan of Shandong University.

Tuesday, January 28, 2020

Tuesday, February 4, 2020

Tuesday, February 11, 2020

Tuesday, February 18, 2020

Tuesday, February 25, 2020

Tuesday, March 3, 2020

Tuesday, March 10, 2020