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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20250110T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-thomas-lesgourgues
SUMMARY:Tutte colloquium-Thomas Lesgourgues
CLASS:PUBLIC
DESCRIPTION:TITLE:Odd-Ramsey numbers of complete bipartite graphs\n\nSPEAKE
 R:\n Thomas Lesgourgues\n\nAFFILIATION:\n University of Waterloo\n\nLOCATI
 ON:\n MC 5501\n\nABSTRACT: In his study of graph codes\, Alon introduced t
 he concept of\nthe odd-Ramsey number of a family of graphs ℋ\, defined 
 as the\nminimum number of colours needed to colour the edges of the comple
 te\ngraph so that every copy of a graph H in ℋ intersects some colour\
 nclass by an odd number of edges. In recent joint work with Simona\nBoyadz
 hiyska\, Shagnik Das\, and Kaline Petrova\, we focus on the\nodd-Ramsey nu
 mbers of complete bipartite graphs. First\, using\npolynomial methods\, we
  completely resolve the problem when ℋ is\nthe family of all spanning 
 complete bipartite graphs on n vertices. We\nthen focus on its subfamilies
 . In this case\, we establish an\nequivalence between the odd-Ramsey probl
 em and a well-known problem\nfrom coding theory\, asking for the maximum d
 imension of a linear\nbinary code avoiding codewords of given weights. We 
 then use known\nresults from coding theory to deduce asymptotically tight 
 bounds in\nour setting. We conclude with bounds for the odd-Ramsey numbers
  of\nfixed (that is\, non-spanning) complete bipartite subgraphs. \n\n \
 n\n 
DTSTAMP:20260405T062120Z
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