Héger, Tamás and Nagy, Zoltán Lóránt (2017) Dominating Sets in Projective Planes. JOURNAL OF COMBINATORIAL DESIGNS, 25 (7). pp. 293-309. ISSN 1063-8539
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Abstract
We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result that shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating set in a projective plane of order q>81 is smaller than 2q+2⌊q⌋+2 (i.e., twice the size of a Baer subplane), then it contains either all but possibly one points of a line or all but possibly one lines through a point. Furthermore, we completely characterize dominating sets of size at most 2q+q+1. In Desarguesian planes, we could rely on strong stability results on blocking sets to show that if a dominating set is sufficiently smaller than 3q, then it consists of the union of a blocking set and a covering set apart from a few points and lines. © 2016 Wiley Periodicals, Inc.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | STABILITY; Convergence of numerical methods; projective plane; blocking set; Dominating set; Finite projective plane; Dominating sets; Combinatorial mathematics; projective planes; Strong stability; A-stability; Domination; nocv1; Incidence graphs; |
| Subjects: | Q Science / természettudomány > Q1 Science (General) / természettudomány általában |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 09 May 2023 14:11 |
| Last Modified: | 09 May 2023 14:11 |
| URI: | http://real.mtak.hu/id/eprint/165142 |
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