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DTSTART;TZID=America/Toronto:20250211T150000
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URL:/combinatorics-and-optimization/events/graphs-and-m
 atroids-seokbeom-kim
SUMMARY:Graphs and Matroids - Seokbeom Kim 
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Structure of tournaments with a forbidden s
 ubtournament\n\nSPEAKER:\n Seokbeom Kim \n\nAFFILIATION:\n KAIST\n\nLOCATI
 ON:\n MC 5479\n\nABSTRACT: For a tournament $S$\, a tournament is $S$-free
  if it has no\nsubtournament isomorphic to $S$. Until now\, there have bee
 n only a\nsmall number of tournaments $S$ such that the complete structure
  of\n$S$-free tournaments is known. \n\nLet $\\triangle(1\, 2\, 2)$ be a 
 tournament obtained from the cyclic\ntriangle by substituting two-vertex t
 ournaments for two of its\nvertices. In this talk\, we present a structure
  theorem for\n$\\triangle(1\, 2\, 2)$-free tournaments\, which was previou
 sly unknown.\nAs an application\, we provide tight bounds for the chromati
 c number as\nwell as the size of the largest transitive subtournament for 
 such\ntournaments.\n\nThis talk is based on joint work with Taite LaGrange
 \, Mathieu\nRundström\, Arpan Sadhukhan\, and Sophie Spirkl.\n 
DTSTAMP:20250516T202426Z
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