Department of

June 2020 July 2020August 2020Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa 1 2 3 4 5 6 1 2 3 4 1 7 8 9 10 11 12 13 5 6 7 8 9 10 11 2 3 4 5 6 7 8 14 15 16 17 18 19 20 12 13 14 15 16 17 18 9 101112 13 14 15 21 22 23 24 25 26 27 19 20 21 22 23 24 25 16 17 18 19 20 21 22 28 29 30 26 27 28 29 30 31 23 24 25 26 27 28 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

Tuesday, April 14, 2020

Tuesday, April 21, 2020

Tuesday, April 28, 2020

Tuesday, May 5, 2020

Tuesday, May 12, 2020

Tuesday, May 19, 2020

Tuesday, May 26, 2020

Tuesday, June 2, 2020

Tuesday, June 9, 2020

Tuesday, June 16, 2020

Tuesday, June 23, 2020

Tuesday, June 30, 2020

Tuesday, July 7, 2020

Tuesday, July 14, 2020

Tuesday, July 21, 2020

Tuesday, July 28, 2020

Tuesday, August 4, 2020

Tuesday, August 11, 2020