Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, November 08, 2022, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Raphael Steiner

Splitting digraphs

This talk will mostly be a short survey of some really beautiful and intriguing open problems related to out-degrees in directed graphs and splittings of digraphs with degree constraints. In particular, I will present and discuss three open problems, (1) a problem proposed by Stiebitz (1995) and also by Alon (2006) regarding splits of digraphs into two induced subgraphs preserving high minimum out-degree, (2) a problem proposed by Alon (2006) and also by Kreutzer, Oum, Seymour, van der Zypen and Wood (2016) regarding splits of digraphs into several induced subgraphs while reducing the maximum out-degree, and (3) a problem by Alon (2006) regarding subgraphs of given size that preserve a high minimum out-degree. I will present the known ideas and partial results, but also give explanations and intuition for why these problems are so much harder than their undirected analogues, which all have relatively simple solutions. I will also present a construction that solves problem (3) in the negative.


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