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X-WR-CALNAME:[gt.go] - 'Shallow vertex minors\, stability\, and dependence'
  by Patrice Ossona de Mendez
X-WR-TIMEZONE:Europe/Paris
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TZUNTIL:20260329T010000Z
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DTSTART:20231029T030000
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TZOFFSETTO:+0100
RDATE:20241027T030000
RDATE:20251026T030000
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DESCRIPTION:/Exposé /Talk/ \n\nStability and dependence are model-theoretic
  notions that have recently proved highly effective in the study of struct
 ural and algorithmic properties of hereditary graph classes\, and are cons
 idered key notions for generalizing to hereditary graph classes the theory
  of sparsity developed for monotone graph classes (where an essential noti
 on is that of nowhere dense class). The theory of sparsity was initially b
 uilt on the notion of shallow minors and on the idea of excluding differen
 t setsof minors\, depending on the depth at which these minors can appear.
  In this talk\, we follow a similar path\, where shallow vertex minors rep
 lace shallow minors. In this setting\, we provide a neat characterization 
 of stable / dependent hereditary classes of graphs: A hereditary class of 
 graphs is dependent if and only if it does not contain all permutation gra
 phs and\, for each integer r\, it excludes some split interval graph as a 
 depth-r vertex minor\; it is stable if and only if\, for each integer r\, 
 it excludes some half-graph as a depth-r vertex minor. A key ingredient in
  proving these results is the preservation of stability and dependence of 
 a class when taking bounded depth shallow vertex minors. \n\n\n[Patrice Os
 sona de Mendez ] (EHESS ) \n[ https://web.math.princeton.edu/~pds/ | http:
 //madezhi.free.fr ] \n\n\nRemarks / Remarques \n\nFind all the information
  of the working group on this [ https://graphesetoptimisation.labri.fr/pmw
 iki.php/Groupe/GT?userlang=en | web page ] . \nRetrouvez toutes les inform
 ations du GT sur cette [ https://graphesetoptimisation.labri.fr/pmwiki.php
 /Groupe/GT | page web ] .
DTSTART;TZID=Europe/Paris:20240524T140000
DTEND;TZID=Europe/Paris:20240524T150000
LOCATION:LaBRI/178 et https://webconf.u-bordeaux.fr/b/mar-ef4-zed
SEQUENCE:0
SUMMARY:[gt.go] - 'Shallow vertex minors\, stability\, and dependence' by P
 atrice Ossona de Mendez
TRANSP:OPAQUE
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