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On the balanced upper chromatic number of finite projective planesBlázsik, 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.Source: Discrete mathematics. - ISSN 0012-365X (Vol. 344, iss. 3, Marth 2021, art. 112266 (8 str.))Type of material - article, component part ; adult, seriousPublish date - 2021Language - englishCOBISS.SI-ID - 45461251
Author
Blázsik, Zoltán L. |
Blokhuis, Aart |
Miklavič, Štefko |
Nagy, Zoltán Lóránt, 1985- |
Szőnyi, Tamás
Topics
projektiovne ravnine |
uravnoteženo zgornje kromatično število |
diferenčne množice |
ravninske funkcije |
verjetnostna metoda |
projective planes |
balanced upper chromatic number |
difference sets |
planar functions |
probabilistic method
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Database name | Field | Year |
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Blázsik, Zoltán L. | |
Blokhuis, Aart | |
Miklavič, Štefko | 21656 |
Nagy, Zoltán Lóránt, 1985- | |
Szőnyi, Tamás | 51192 |
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