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  • On the balanced upper chromatic number of finite projective planes
    Blázsik, Zoltán L. ...
    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 G. Araujo-Pardo et al. [ibid. 338, No. 12, 2562--2571 (2015)] by determining the balanced upper chromatic number of the desarguesian projective plane ▫$\operatorname{PG} ( 2 , q )$▫ for all ▫$q$▫. In addition, we determine asymptotically the balanced upper chromatic number of several families of non-desarguesian 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.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 344, iss. 3, Marth 2021, art. 112266 (8 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 45461251

    Povezava(-e):

    https://www.sciencedirect.com/science/article/abs/pii/S0012365X20304520
    Repozitorij Univerze na Primorskem - RUP
    DOI

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 344, iss. 3, Marth 2021, art. 112266 (8 str.))
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