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(1)
Convex Polygon
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Convex Polygons are CoverDecomposable
Convex Polygons are CoverDecomposable,10.1007/s004540099133y,Discrete & Computational Geometry,Dömötör Pálvölgyi,Géza Tóth
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Convex Polygons are CoverDecomposable
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Citations: 6
)
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Dömötör Pálvölgyi
,
Géza Tóth
We show that for any open
convex polygon
P, there is a constant k(P) such that any k(P)fold covering of the plane with translates of P can be decomposed into two coverings.
Journal:
Discrete & Computational Geometry  DCG
, vol. 43, no. 3, pp. 483496, 2010
DOI:
10.1007/s004540099133y
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Citation Context
(5)
...Finally, a very recent result due to Pálvölgyi and Tóth [
8
] shows that any convex polygon is coverdecomposable...
...The constant c in the results of [4] and [
8
] depends on the convex polygon, in particular the number of its sides, and that is why these results say nothing about the original conjecture of Pach on the coverdecomposability of an arbitrary convex set...
Matt Gibson
,
et al.
Optimally Decomposing Coverings with Translates of a Convex Polygon
...Theorem C (Pálvölgyi and Tóth [
9
]) Every open convex polygon is coverdecomposable...
...Theorem E (Pálvölgyi and Tóth [
9
]) Every open polygon that has no special pair of wedges is totallycoverdecomposable...
Dömötör Pálvölgyi
.
Indecomposable Coverings with Concave Polygons
...These functions have been the focus of many recent research papers and some special cases are resolved. See, e.g., [1,2,6,11,12,13,15,
16
,17]...
Shakhar Smorodinsky
,
et al.
Polychromatic Coloring for HalfPlanes
...Finally, a very recent result due to P´alv¨olgyi and T´oth [
11
] shows that any convex polygon is coverdecomposable...
...The constant c in the results of [8] and [
11
] depends on the convex polygon, in particular the number of its sides, and that is why these results say nothing about the original conjecture of Pach...
Matt Gibson
,
et al.
Decomposing Coverings and the Planar Sensor Cover Problem
...Note that for translates of an arbitrary open convex polygon, Pálvölgyi and Tóth recently proved that there exists a constant c such that cfold coverings can be decomposed into two coverings [
15
]...
Greg Aloupis
,
et al.
Decomposition of Multiple Coverings into More Parts
References
(9)
Decomposition of Multiple Coverings into More Parts
(
Citations: 10
)
Greg Aloupis
,
Jean Cardinal
,
Sébastien Collette
,
Stefan Langerman
,
David Orden
,
Pedro Ramos
Journal:
Discrete & Computational Geometry  DCG
, vol. 44, no. 3, pp. 706723, 2008
Research problems in discrete geometry
(
Citations: 216
)
Peter Brass
,
William O. J. Moser
,
János Pach
Published in 2005.
Decomposition of multiple packing and covering
(
Citations: 23
)
J. Pach
Published in 1980.
Covering the Plane with Convex Polygons
(
Citations: 16
)
János Pach
Journal:
Discrete & Computational Geometry  DCG
, vol. 1, no. 1, pp. 7381, 1986
Decomposition of multiple coverings into many parts
(
Citations: 20
)
János Pach
,
Géza Tóth
Conference:
Symposium on Computational Geometry  SOCG
, pp. 133137, 2007
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Citations
(6)
Optimally Decomposing Coverings with Translates of a Convex Polygon
Matt Gibson
,
Kasturi Varadarajan
Journal:
Discrete & Computational Geometry  DCG
, vol. 46, no. 2, pp. 313333, 2011
Indecomposable Coverings with Concave Polygons
(
Citations: 6
)
Dömötör Pálvölgyi
Journal:
Discrete & Computational Geometry  DCG
, vol. 44, no. 3, pp. 577588, 2010
Polychromatic Coloring for HalfPlanes
(
Citations: 1
)
Shakhar Smorodinsky
,
Yelena Yuditsky
Conference:
Scandinavian Workshop on Algorithm Theory  SWAT
, pp. 118126, 2010
Decomposition of Geometric Set Systems and Graphs
Dömötör Pálvölgyi
Journal:
Computing Research Repository  CORR
, vol. abs/1009.4, 2010
Decomposing Coverings and the Planar Sensor Cover Problem
(
Citations: 8
)
Matt Gibson
,
Kasturi R. Varadarajan
Journal:
Computing Research Repository  CORR
, vol. abs/0905.1, pp. 159168, 2009