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DTSTART:20270328T030000
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DTSTAMP:20261110T151024Z
UID:1794925800@ist.ac.at
DTSTART:20261117T153000
DTEND:20261117T162000
DESCRIPTION:Speaker: Yuval Wigderson\nhosted by Matthew Kwan\nAbstract: A s
 imple exercise appearing in many graph theory courses is that if a graph h
 as minimum degree d\, then it contains a cycle of length at least d+1. A s
 ubstantially more challenging generalization of this is a celebrated theor
 em of Erds and Gallai\, which states that the same conclusion holds if we 
 only assume that the average degree is d. Although the Erds–Gallai theo
 rem has a relatively short proof\, I personally find it somewhat mysteriou
 s and unenlightening. In this talk\, I will discuss a new proof of the Erd
 s–Gallai theorem\, which has the disadvantages of being a lot more compl
 icated and of proving a somewhat weaker statement. However\, its advantage
 s are (a) that it sheds more light on why such a statement should be true\
 , and (b) that it can also be used to prove some interesting and surprisin
 g generalizations. Along the way\, I will discuss a remarkable recent resu
 lt of Pokrovskiy\, which reveals a great deal about the structure of spars
 e graphs. Based on joint work with Micha Christoph and Alp Müyesser.
LOCATION:Raiffeisen Lecture Hall\, ISTA
ORGANIZER:Stephanie.Dolot@ista.ac.at
SUMMARY:Yuval Wigderson: Long cycles in graphs 
URL:https://talks-calendar.ista.ac.at/events/6759
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