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X-WR-CALNAME:[gt.go] - 'Random embeddings of bounded degree trees with opti
 mal spread' by Clément Legrand-Duchesne
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TZUNTIL:20251026T010000Z
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DTSTART:20231029T030000
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RDATE:20241027T030000
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DESCRIPTION:/Exposé /Talk/ \n\nA seminal result of Komlos\, Sarkozy and Sze
 meredi proves that for any \Delta and \alpha\, any graph G with minimum de
 gree (1/2+\alpha)n and large enough n contains all n-vertex trees of maxim
 um degree \Delta. Given two graphs H and G\, recent advances on the Kahn-K
 alai conjecture connect the existence of /spread measures/ on the space of
  embeddings of H in G\, with the probabilistic threshold above which a ran
 dom subgraph of G\, obtained by sampling the edges at a fixed rate\, still
  contains H with good probability. Spread distributions also give a lower 
 bound on the number of embeddings of H in G. In 2023\, Pham\, Sah\, Sawhne
 y and Simkin designed a spread measure on the embeddings of bounded degree
  trees in graphs of minimum degree (1/2+\alpha)n\, by following the proof 
 of Komlos /et al/. \n\nWe give a regularity free proof of this result. As 
 a result\, we obtain much better constants\, with a more flexible framewor
 k and unlike the proof of Pham /et al./\, our construction generalises to 
 hypergraphs and digraphs painlessly. \n\nThis is joint work with Paul Bast
 ide and Alp Müyesser. \n\n\n[Clément Legrand-Duchesne] (Université de Bord
 eaux\, LaBRI ) \nhttps://www.labri.fr/perso/clemlegrand/ \n\n\nRemarks / R
 emarques \n\nFind all the information of the working group on this [ https
 ://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT?userlang=en | web p
 age ] . \nRetrouvez toutes les informations du GT sur cette [ https://grap
 hesetoptimisation.labri.fr/pmwiki.php/Groupe/GT | page web ] .
DTSTART;TZID=Europe/Paris:20240119T140000
DTEND;TZID=Europe/Paris:20240119T150000
LOCATION:LaBRI/178
SEQUENCE:0
SUMMARY:[gt.go] - 'Random embeddings of bounded degree trees with optimal s
 pread' by Clément Legrand-Duchesne
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