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

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

Duration: 30 minutes

Location: OAT S15/S16/S17

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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