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The Probabilistic Method
The use of randomness is now an accepted tool in Theoretical Computer Science but not everyone is aware of the underpinnings of this methodology in Combinatorics - particularly, in what is now called the probabilistic Method as developed primarily by Paul Erdoős. Expand
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The degree sequence of a scale-free random graph process
A random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. Expand
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Edge disjoint placement of graphs
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Lopsided Lovász Local Lemma and Latin transversals
A new version of the Lovasz Local lemma is used to prove the existence of Latin transversals in matrices where no symbol appears too often. Expand
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Sudden Emergence of a Giantk-Core in a Random Graph
Thek-core of a graph is the largest subgraph with minimum degree at leastk. For the Erdo?s?R?nyi random graphG(n,?m) onnvertives, withmedges, it is known that a giant 2-core grows simultaneously with a giant component, that is, whenmis close ton/2. We show that fork?3, with high probability, a giant k-core appears suddenly. Expand
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Asymptotic lower bounds for Ramsey functions
  • J. Spencer
  • Computer Science, Mathematics
  • Discret. Math.
  • 1977
A probability theorem, due to Lovasz, is used to derive lower bounds for various Ramsey functions. Expand
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Six standard deviations suffice
Given n sets on n elements it is shown that there exists a two-coloring such that all sets have discrepancy at most Knl/2, K an absolute constant. This improves the basic probabilistic method withExpand
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Intersection theorems for systems of sets
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Asymptotic behavior of the chromatic index for hypergraphs
Abstract We show that if a collection of hypergraphs (1) is uniform (every edge contains exactly k vertices, for some fixed k ), (2) has minimum degree asymptotic to the maximum degree, and (3) hasExpand
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Ten lectures on the probabilistic method
This is an examination of what is known about the probabilistic method. Based on the notes from the author's 1986 series of ten lectures, this edition features an additional lecture: The JansonExpand
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