Indecomposable Coverings

János Pach, Gábor Tardos, Géza Tóth

Research output: Chapter in Book/Report/Conference proceedingConference contribution

33 Citations (Scopus)

Abstract

We prove that for every k > 1, there exist k-fold coverings of the plane (1) with strips, (2) with axis-parallel rectangles, and (3) with homothets of any fixed concave quadrilateral, that cannot be decomposed into two coverings. We also construct, for every k > 1, a set of points P and a family of disks in the plane, each containing at least k elements of P, such that no matter how we color the points of P with two colors, there exists a disk , all of whose points are of the same color.

Original languageEnglish
Title of host publicationDiscrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers
Pages135-148
Number of pages14
DOIs
Publication statusPublished - Dec 1 2007
Event7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an, China
Duration: Nov 22 2005Nov 24 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4381 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005
CountryChina
CityXi'an
Period11/22/0511/24/05

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Pach, J., Tardos, G., & Tóth, G. (2007). Indecomposable Coverings. In Discrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers (pp. 135-148). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4381 LNCS). https://doi.org/10.1007/978-3-540-70666-3_15