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URL:/combinatorics-and-optimization/events/graphs-and-m
 atroids-seminar-dao-chen-yuan
SUMMARY:Graphs and Matroids Seminar - Dao Chen Yuan
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Chromatic Number of Random Signed Graphs\n\n
 SPEAKER:\n Dao Chen Yuan\n\nAFFILIATION:\n University of À¶Ý®ÊÓƵ\n\nLOCAT
 ION:\n MC 5417\n\nABSTRACT: A signed graph is a graph where edges are labe
 lled {+1\,-1}.\nA signed colouring in 2k colours maps the vertices of a si
 gned graph\nto {-k\,...\,-1\,1\,...\,k}\, such that neighbours joined by a
  positive edge\ndo not share the same colour\, and those joined by a negat
 ive edge do\nnot share opposite colours. It is a classical result that the
 \nchromatic number of a G(n\,p) Erdos-Renyi random graph is\nasymptoticall
 y almost surely n/(2log_b(n))\, where p is constant and\nb=1/(1-p). We ext
 end the method used there to prove that the chromatic\nnumber of a G(n\,p\
 ,q) random signed graph\, where q is the probability\nthat an edge is labe
 lled -1\, is also a.a.s. n/(2log_b(n))\, if p is\nconstant and q=o(1).\n 
DTSTAMP:20250520T220031Z
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