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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-lap-chi-lau-0
SUMMARY:Tutte Colloquium - Lap Chi Lau
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Cheeger Inequalities for Vertex Expansion an
 d Reweighted\nEigenvalues\n\nSpeaker:\n Lap Chi Lau\n\nAffiliation:\n Univ
 ersity of À¶Ý®ÊÓƵ\n\nLocation:\n MC 5501\n\nABSTRACT: \n\nThe classical C
 heeger's inequality relates the edge conductance $\\phi$\nof a graph and t
 he second smallest eigenvalue $\\lambda_2$ of the\nLaplacian matrix. Recen
 tly\, Olesker-Taylor and Zanetti discovered a\nCheeger-type inequality $\\
 psi^2 / \\log |V| \\lesssim \\lambda_2^*\n\\lesssim \\psi$ connecting the 
 vertex expansion $\\psi$ of a graph\n$G=(V\,E)$ and the maximum reweighted
  second smallest eigenvalue\n$\\lambda_2^*$ of the Laplacian matrix. In th
 is work\, we first improve\ntheir result to $\\psi^2 / \\log d \\lesssim \
 \lambda_2^* \\lesssim \\psi$\nwhere $d$ is the maximum degree in $G$\, whi
 ch is optimal assuming the\nsmall-set expansion conjecture. Also\, the imp
 roved result holds for\nweighted vertex expansion\, answering an open ques
 tion by\nOlesker-Taylor and Zanetti. \n 
DTSTAMP:20250919T085043Z
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