Year: 2026
Type: preprint
Abstract: An arrangement of $n$ lines in the plane defines cells, i.e., connected components of the complement of the arrangement. Answering a question of Volkmar Welker we show that, apart from two special cases, there is always a line $L$ in the arrangement such that one of the open halfplanes whose boundary is $L$ contains more than half of the bounded cells of the arrangement. We also consider some unusual discrepancy problems that are related to this question.
Source: arXiv (Cornell University)
Author: Bárány, Imre
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214055472
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