Blázsik, L. Zoltán and Blokhuis, Aart and Miklavic, Stefko and Nagy, Zoltán Lóránt and Szőnyi, Tamás (2021) On the balanced upper chromatic number of finite projective planes. DISCRETE MATHEMATICS, 344 (3). ISSN 0012365X

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Abstract
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 (rainbowfree colorings). For any hypergraph H, the maximum number k for which there is a balanced rainbowfree kcoloring of H is called the balanced upper chromatic number of the hypergraph. We confirm the conjecture of AraujoPardo, Kiss and Montejano by determining the balanced upper chromatic number of the desarguesian projective plane PG(2,q) for all q. In addition, we determine asymptotically the balanced upper chromatic number of several families of nondesarguesian projective planes and also provide a general lower bound for arbitrary projective planes using probabilistic methods which determines the parameter up to a multiplicative constant.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA166QA166.245 Graphs theory / gráfelmélet Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria 
Depositing User:  Zoltán L. Blázsik 
Date Deposited:  22 Dec 2021 12:51 
Last Modified:  03 Apr 2023 07:32 
URI:  http://real.mtak.hu/id/eprint/134900 
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