On point covers of multiple intervals and axis-parallel rectangles

Abstract

In certain families of hypergraphs the transversal number is bounded by some function of the packing number. In this paper we study hypergraphs related to multiple intervals and axisparallel rectangles, respectively. Essential improvements of former established upper bounds are presented here. We explore the close connection between the two problems at issue.

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Supported by the Alexander von Humboldt Foundation and the NSF grant No. STC-91-19999

Supported by the NSF grant No. CCR-92-00788, the (Hungarian) National Scientific Research Fund (OTKA) grant No. F014919. The author was visiting the Computation and Automation Institute, Budapest while part of this research was done.

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Károlyi, G., Tardos, G. On point covers of multiple intervals and axis-parallel rectangles. Combinatorica 16, 213–222 (1996). https://doi.org/10.1007/BF01844847

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Mathematics Subject Classification (1991)

  • 05 C 65
  • 05 C 70
  • 05 C 35