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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240325T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-eero-raty
SUMMARY:Algebraic Graph Theory - Eero Räty
CLASS:PUBLIC
DESCRIPTION:TITLE: Positive discrepancy\, MaxCut and eigenvalues of graphs\
 n\nSPEAKER:\n Eero Räty\n\nAFFILIATION:\n University of Umeå\n\nLOCATION
 :\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT: The positive
  discrepancy of a graph G of edge density p is\ndefined as the maximum of 
 e(U) - p|U|(|U|-1)/2\, where the maximum is\ntaken over subsets of vertice
 s in G. In 1993 Alon proved that if G is\nd-regular graph on n vertices an
 d d = O(n^(1/9))\, then the positive\ndiscrepancy of G is at least c*d^(1/
 2)n for some constant c.\n\nWe extend this result by proving lower bounds 
 for the positive\ndiscrepancy with average degree d when d < (1/2 - \\epsi
 lon)*n. We\nprove that the same lower bound remains true when d < n^(2/3)\
 , while\nin the ranges n^(2/3) < d < n^(4/5) and n^(4/5) < d < (1/2 -\n\\e
 psilon)*n we prove that the positive discrepancy is at least n^2/d\nand d^
 (1/4)n/log(n) respectively.
DTSTAMP:20260404T213639Z
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