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Orientations of cycles in digraphs of high chromatic number and high minimum out-degree

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arxiv 2503.20045 v1 pith:ADQIVS5T submitted 2025-03-25 math.CO

Hidde Koerts , Benjamin Moore , Sophie Spirkl This is my paper · ORCID
classification math.CO
keywords cycleseveryhighminimumorientationsout-degreevarepsilonarcs
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abstract

We characterize all orientations of cycles $C$ for which for every fixed $\varepsilon > 0$ there exists a constant $c \geq 1$ such that every digraph $D$ without loops or parallel arcs with $\chi(D) \geq c$ and minimum out-degree at least $\varepsilon |V(D)|$ contains $C$ as a subdigraph. This generalizes a result of Thomassen.

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  1. A directed Andr\'asfai-Erd\H{o}s-S\'os theorem and chromatic profiles of oriented cycles

    math.CO 2025-09 conditional novelty 8.0 of 10

    For every r≥3, the exact chromatic profile of the transitive tournament T_r is (3r-7)/(3r-4); directed odd cycles have 2-color profile 1/2, and the three non-directed pentagon orientations have 2-color profile 1/3.

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