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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240610T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-john-byrne
SUMMARY:Algebraic Graph Theory - John Byrne
CLASS:PUBLIC
DESCRIPTION:TITLE: A general theorem in spectral extremal graph theory\n\n
 SPEAKER:\n John Byrne\n\nAFFILIATION:\n University of Delaware\n\nLOCATION
 :\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT: The extremal 
 graphs $\\mathrm{EX}(n\,\\mathcal F)$ and\nspectral extremal graphs $\\mat
 hrm{SPEX}(n\,\\mathcal F)$ are the sets of\ngraphs on $n$ vertices with ma
 ximum number of edges and maximum\nspectral radius\, respectively\, with n
 o subgraph in $\\mathcal F$. We\nprove a general theorem which allows us t
 o characterize the spectral\nextremal graphs for a wide range of forbidden
  families $\\mathcal F$\nand implies several new and existing results. In 
 particular\, whenever\n$\\mathrm{EX}(n\,\\mathcal F)$ contains the complet
 e bipartite graph\n$K_{k\,n-k}$ (or certain similar graphs) then $\\mathrm
 {SPEX}(n\,\\mathcal\nF)$ contains the same graph when $n$ is sufficiently 
 large. We prove a\nsimilar theorem which relates $\\mathrm{SPEX}(n\,\\math
 cal F)$ and\n$\\mathrm{SPEX}_\\alpha(n\,\\mathcal F)$\, the set of $\\math
 cal F$-free\ngraphs which maximize the spectral radius of the matrix\n$A_\
 \alpha=\\alpha D+(1-\\alpha)A$\, where $A$ is the adjacency matrix and\n$D
 $ is the diagonal degree matrix.
DTSTAMP:20260403T082116Z
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