Springe direkt zu Inhalt

# 2020/2021

Talks normally take place Wednesdays or Thursdays.

DateSpeakerTitle
02.12.2020 Ander Lamaison
(Masaryk University Brno)
TBA
26.11.2020 Anurag Bishnoi
(TU Delft)
Lower bounds for diagonal Ramsey numbers
18.11.2020 Raphael Steiner
(TU Berlin)
Disjoint cycles of distinct lengths in directed graphs of large connectivity or large minimum degree
12.11.2020 Tibor Szabó
(FU Berlin)
04.11.2020 Alp Müyesser
(FU Berlin)
A rainbow version of Hajnal-Szemerédi Theorem
02.12.2020
Ander Lamaison (Masaryk University Brno)
TBA

Abstract: tba

26.11.2020
Anurag Bishnoi (TU Delft)
Lower bounds for diagonal Ramsey numbers

Abstract: In a recent breakthrough Conlon and Ferber gave an exponential improvement in the lower bounds on diagonal Ramsey number R(t, t, \dots, t), when the number of colours is at least 3. We discuss their construction, along with the further improvement of Wigderson, and the finite geometry behind it.

18.11.2020
Raphael Steiner (TU Berlin)
Disjoint cycles of distinct lengths in directed graphs of large connectivity or large minimum degree

Abstract: A classical result by Thomassen from 1983 states that for every k ≥1 there is an integer f(k) such that every digraph with minimum out-degree f(k) contains k vertex-disjoint directed cycles. The known proof methods for Thomassen's result however do not give any information concerning the lengths of the k disjoint cycles.

In undirected graphs, it is true that sufficiently large minimum degree guarantess k disjoint cycles of equal lengths, as shown by Alon (1996), and also k disjoint cycles of distinct lengths, as shown by Bensmail et al (2017). Alon also gave a construction showing that there are digraphs of unbounded minimum out- and in-degree containing no k disjoint directed cycles of the same length.

In 2014 Lichiardopol made the following conjecture: For every k there exists an integer g(k) such that every digraph of minimum out-degree g(k) contains k vertex-disjoint directed cycles of pairwise distinct lengths.

This conjecture seems quite challenging, as already the existence of g(3) is unknown. For general k the conjecture is only proved in some special cases such as tournaments and regular digraphs by Bensmail et al. (2017).

In my talk I will present some recent ideas for finding disjoint cycles of distinct lengths in digraphs based on a new tool from structural digraph theory. I have the following partial results.

For every k there exists an integer s(k) such that every strongly s(k)-connected digraph contains k vertex-disjoint directed cycles of pairwise distinct lengths.

There exists an integer K such that every digraph of minimum out- and in-degree at least K contains 3 vertex-disjoint directed cycles of pairwise distinct lengths.

12.11.2020
Tibor Szabó (FU Berlin)