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Primitive Illumination Systems for Families of Convex Bodies in the Plane

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Abstract

Let F= {C1,C2,...,C} be a family of ndisjoint convex bodies in the plane. We say that a set Vof exterior light sources illuminates F, if for every boundary point ν of any member of Fthere is a point ν in Vsuch that υ is visible from ν,i.e. the open line segment joining ν and υ is disjoint from ∪ F. An illumination system Vis called primitive if no proper subset of Villuminates F. Let pmax(F) denote the maximum number of points forming a primitive illumination system for F, and letpmax(n) denote the minimum of F) taken over all families Fconsisting of ndisjoint convex bodies in the plane. The aim of this paper is to investigate the quantities pmax(F) and pmax(n).

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References

  1. Boltjansky, V. G. and Gohberg, Y.: Results and Problems in Combinatorial Geometry, Cambridge University Press, 1985.

  2. Boltjansky, V. G. and Soltan, P. S.: Combinatorial Geometry of Various Classes of Convex Sets(in Russian), Ş tiinţa, ChişinĂu, 1978.

  3. Czyzowicz, J., Rivera–Campo, E. and Urrutia, J.: Illuminating rectangles and triangles in the plane, J. Combin. Theory Ser. B. 57(1993), 1–17.

    Google Scholar 

  4. Fejes Tóth, L.: Illumination of convex discs, Acta Math. Acad. Sci. Hungar. 29(1977), 355–360.

    Google Scholar 

  5. Soltan, V.: External illumination according to L. Fejes T´oth, Studia Sci. Math. Hungar. 28(1993), 473–483.

    Google Scholar 

  6. Valentine, F. A.: Visible shorelines, Amer. Math. Monthly 77(1970), 146–152.

    Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, Moldavian Academy of Science, Str. Academiei 5, 277028, Chişinău, Moldova

    VALERIU SOLTAN

  2. Computer and Automation Institute, Hungarian Academy of Sciences, 1111 Budapest, Kende utca, 13–17, Hungary

    LÁSZLÓ SZABÓ

  3. Department of Geometry, Eötvös Loránd University, 1088, Budapest, Rákóczi út 5, Hungary

    ÉVA VÁSÁRHELYI

Authors
  1. VALERIU SOLTAN
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  2. LÁSZLÓ SZABÓ
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  3. ÉVA VÁSÁRHELYI
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SOLTAN, V., SZABÓ, L. & VÁSÁRHELYI, É. Primitive Illumination Systems for Families of Convex Bodies in the Plane. Geometriae Dedicata 66, 125–148 (1997). https://doi.org/10.1023/A:1004932610287

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  • DOI: https://doi.org/10.1023/A:1004932610287

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