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arXiv · 2508.16043

Acyclic and complete coloring of digraphs with the minimum and maximum possible numbers of colors

Mika Olsen·Christian Rubio-Montiel·Alejandra Silva Ramirez
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Abstract

The dichromatic and diachromatic numbers of a digraph are the minimum and maximum numbers of colors, respectively, in acyclic and complete colorings of the digraph. In this paper, we construct, for all $r \leq t$, non-symmetric digraphs with dichromatic number $r$ and diachromatic number $t$. Moreover, we discuss the existence of asymmetric digraphs with dichromatic number $ r $ and diachromatic number $ t \geq r $, establishing a quadratic upper bound $ b(r) \leq t $.

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Mika Olsen, Christian Rubio-Montiel, Alejandra Silva Ramirez. 2025-08-22. Acyclic and complete coloring of digraphs with the minimum and maximum possible numbers of colors. https://arxiv.org/abs/2508.16043

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