Dominating Sets in Projective Planes
| Autor: | H��ger, Tam��s, Nagy, Zolt��n L��r��nt |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | J COMB DES JOURNAL OF COMBINATORIAL DESIGNS. |
| Popis: | We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result which 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 $2q+2[\sqrt{q}]+2$ (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 $2q+\sqrt{q}+1$. 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. 19 pages |
| Databáze: | OpenAIRE |
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