A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are cover-decomposable. Here we show that closed, centrally symmetric convex polygons are also cover-decomposable. We also show that an infinite-fold covering of the plane with translates of $P$ can be decomposed into two infinite-fold coverings. Both results hold for coverings of any subset of the plane.
@article{10_37236_4227,
author = {Istv\'an Kov\'acs and G\'eza T\'oth},
title = {Multiple coverings with closed polygons},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4227},
zbl = {1308.52014},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4227/}
}
TY - JOUR
AU - István Kovács
AU - Géza Tóth
TI - Multiple coverings with closed polygons
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4227/
DO - 10.37236/4227
ID - 10_37236_4227
ER -
%0 Journal Article
%A István Kovács
%A Géza Tóth
%T Multiple coverings with closed polygons
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4227/
%R 10.37236/4227
%F 10_37236_4227
István Kovács; Géza Tóth. Multiple coverings with closed polygons. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4227
