# On the balanced upper chromatic number of finite projective planes

@article{Blzsik2021OnTB, title={On the balanced upper chromatic number of finite projective planes}, author={Zolt{\'a}n L. Bl{\'a}zsik and Aart Blokhuis and {\vS}tefko Miklavi{\vc} and Zolt{\'a}n L{\'o}r{\'a}nt Nagy and Tam{\'a}s Szonyi}, journal={Discret. Math.}, year={2021}, volume={344}, pages={112266} }

In this paper, we study vertex colorings of hypergraphs in which all color class sizes differ by at most one (balanced colorings) and each hyperedge contains at least two vertices of the same color (rainbow-free colorings). For any hypergraph $H$, the maximum number $k$ for which there is a balanced rainbow-free $k$-coloring of $H$ is called the balanced upper chromatic number of the hypergraph. We confirm the conjecture of Araujo-Pardo, Kiss and Montejano by determining the balanced upper…

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