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CPC
2016

Decomposition of Multiple Packings with Subquadratic Union Complexity

4 years 3 months ago
Decomposition of Multiple Packings with Subquadratic Union Complexity
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.
János Pach, Bartosz Walczak
Added 01 Apr 2016
Updated 01 Apr 2016
Type Journal
Year 2016
Where CPC
Authors János Pach, Bartosz Walczak
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