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SUMMARY:Tibor Szabó (Berlin)
DTSTART:20201113T140000Z
DTEND:20201113T150000Z
DTSTAMP:20260423T020958Z
UID:WCS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WCS/10/">Mad
 er-perfect digraphs</a>\nby Tibor Szabó (Berlin) as part of Warwick Combi
 natorics Seminar\n\n\nAbstract\nWe investigate the relationship of dichrom
 atic number and subdivision containment in digraphs. We call a digraph Mad
 er-perfect if for every (induced) subdigraph $F$\, any digraph of dichroma
 tic number at least $v(F)$ contains an $F$-subdivision. We show that\, amo
 ng others\, arbitrary orientated cycles\, bioriented trees\, and tournamen
 ts on four vertices are Mader-perfect. The first result settles a conjectu
 re of Aboulker\, Cohen\, Havet\, Lochet\, Moura\, and Thomasse\, while the
  last one extends Dirac's Theorem about $4$-chromatic graphs containing a 
 $K_4$-subdivision to directed graphs. The talk represents joint work with 
 Lior Gishboliner and Raphael Steiner.\n
LOCATION:https://researchseminars.org/talk/WCS/10/
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