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1.
Nonuniform lines on finite projective planes
Ádám Markó, 2026, original scientific article

Abstract: We consider the stability version of the following problem, originally posed by Erdős: colour the points of a projective plane of order q, q odd, with two colours. What is the minimum number of nonuniform lines, that is the lines on which the number of points of the two colours are not the same. It is easy to show that the number of nonuniform lines is at least q+1 and there is a trivial colouring with q+1 nonuniform lines. Our main result is that the number of nonuniform lines is at least 13/8 * q or we have the trivial colouring.
Keywords: colouring, projective planes, blocking sets
Published in RUP: 20.03.2026; Views: 169; Downloads: 3
.pdf Full text (414,61 KB)

2.
On the balanced upper chromatic number of finite projective planes
Zoltán L. Blázsik, Aart Blokhuis, Štefko Miklavič, Zoltán Lóránt Nagy, Tamás Szőnyi, 2021, original scientific article

Keywords: projective planes, balanced upper chromatic number, difference sets, planar functions, probabilistic method
Published in RUP: 18.01.2021; Views: 2746; Downloads: 40
URL Link to full text

3.
On the spectrum of the sizes of semiovals in PG (2,q), q odd
György Kiss, Stefano Marcugini, Fernanda Pambianco, 2010, published scientific conference contribution

Keywords: semiovals, projective planes, nontangent lines, bounds, secants
Published in RUP: 08.08.2016; Views: 4238; Downloads: 113
URL Link to full text

4.
On the balanced upper chromatic number of cyclic projective planes and projective spaces
Gabriela Araujo-Pardo, György Kiss, Amanda Montejano, 2015, original scientific article

Keywords: balanced rainbow-free colorings, upper chromatic number, projective planes, projective spaces
Published in RUP: 08.08.2016; Views: 4209; Downloads: 175
URL Link to full text

5.
On the intersection of Baer subgeometries of PG(n, q[sup]2)
Izabella Jagos, György Kiss, Attila Pór, 2003, original scientific article

Keywords: Baer subgeometries, finite projective spaces, non-desarguesian translation planes
Published in RUP: 08.08.2016; Views: 5399; Downloads: 90
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