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On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed | Carlos A. Alfaro
; Adrián Vázquez-Ávila
; | Date: |
6 Oct 2017 | Abstract: | For $rgeq2$, let $(P,mathcal{L})$ be an $r$-uniform linear system. The
transversal number $ au(P,mathcal{L})$ of $(P,mathcal{L})$ is the minimum
number of points that intersect every line of $(P,mathcal{L})$. The 2-packing
number $
u_2(P,mathcal{L})$ of $(P,mathcal{L})$ is the maximum number of
lines such that the intersection of any three of them is empty. In [Discrete
Math. 313 (2013), 959--966] Henning and Yeo posed the following question: Is it
true that if $(P,mathcal{L})$ is a $r$-uniform linear system then
$ au(P,mathcal{L})leqdisplaystylefrac{|P|+|mathcal{L}|}{r+1}$ holds for
all $kgeq2$?. In this paper, some results about of $r$-uniform linear systems
whose 2-packing number is fixed which satisfies the inequality are given. | Source: | arXiv, 1710.2501 | Services: | Forum | Review | PDF | Favorites |
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