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CPC
2016
8 years 7 months ago
On the Length of a Random Minimum Spanning Tree
We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen ...
Colin Cooper, Alan M. Frieze, Nate Ince, Svante Ja...
CPC
2016
8 years 7 months ago
On the Chromatic Thresholds of Hypergraphs
József Balogh, Jane Butterfield, Ping Hu, J...
CPC
2016
8 years 7 months ago
Forcing a sparse minor
This paper addresses the following question for a given graph H: what is the minimum number f(H) such that every graph with average degree at least f(H) contains H as a minor? Due...
Bruce A. Reed, David R. Wood
CPC
2016
8 years 7 months ago
The Satisfiability Threshold for k-XORSAT
We consider “unconstrained” random k-XORSAT, which is a uniformly random system of m linear non-homogeneous equations in F2 over n variables, each equation containing k ≥ 3 v...
Boris Pittel, Gregory B. Sorkin
CPC
2016
8 years 7 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...
János Pach, Bartosz Walczak
CPC
2016
8 years 7 months ago
On Active and Passive Testing
Given a property of Boolean functions, what is the minimum number of queries required to determine with high probability if an input function satisfies this property? This is a f...
Noga Alon, Rani Hod, Amit Weinstein