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Turán problems in directed and mixed graphs

Connections Workshop: Extremal Combinatorics February 06, 2025 - February 07, 2025

February 07, 2025 (11:15 AM PST - 12:15 PM PST)
Speaker(s): Nitya Mani (Massachusetts Institute of Technology)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Turán problems in directed and mixed graphs

Abstract

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We investigate natural Turán problems for directed graphs (digraphs) and mixed graphs, generalizations of graphs where edges can be either directed or undirected. In both of these situations, far less is known than in the classical Turán setting. We characterize the Turán numbers of several natural families of sparse digraphs that highlight that directed path lengths play a weaker, but analogous role to the chromatic number in the directed setting. In the mixed graph setting, we study a natural Turán density coefficient, establishing an analogue of the Erdős-Stone-Simonovits theorem and showing that Turán density coefficients can be irrational, but are always algebraic.

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Turán problems in directed and mixed graphs

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