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CPC

2016

2016

Let k be a positive integer and let X be a k-fold packing of inﬁnitely many simply connected compact sets in the plane, that is, assume that every point belongs to at most k sets. Suppose that there is a function f(n) = o(n2 ) with the property that any n members of X surround at most f(n) holes, which means that the complement of their union has at most f(n) connected components. We use tools from extremal graph theory and the topological Helly theorem to prove that X can be decomposed into at most p packings, where p is a constant depending only on k and f.

Added |
01 Apr 2016 |

Updated |
01 Apr 2016 |

Type |
Journal |

Year |
2016 |

Where |
CPC |

Authors |
János Pach, Bartosz Walczak |

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