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UID:ffc6a5294e5143c268a4836008a367a1
CATEGORIES:Discrete Math
CREATED:20250226T141541
SUMMARY:Richard Montgomery - Finding regular subgraphs
LOCATION:Hill 705
DESCRIPTION:Speaker: Richard Montgomery (https://rhmontgomery.warwick.ac.uk/) (Warwick,
IAS)\nTitle: Finding regular subgraphs\nAbstract: Finding regular subgrap
hs can be useful. Many results assume a graph is regular or are easier to p
rove when they are. In 1975, Erdős and Sauer asked for an estimate, for any
constant r, on the maximum number of edges an n-vertex graph can have with
out containing an r-regular subgraph (one in which each vertex is in r edge
s). The best upper bound on this problem was for a long time one of Pyber f
rom 1985, but the last few years have seen rapid developments, initiated by
Janzer and Sudakov, and we now have an efficient framework to find regular
subgraphs for not only constant r but the whole range of possible values o
f r.\n\nI will discuss this framework and its components, which include alg
ebraic techniques of Alon, Friedland and Kalai, the recent breakthroughs on
the sunflower conjecture, techniques to find almost-regular subgraphs deve
loped from Pyber’s work, and, crucially, a novel random process that effici
ently finds a very nearly regular subgraph in any almost-regular graph.\n \
nJoint work with Debsoumya Chakraborti, Oliver Janzer and Abhishek Methuku.
\n\n
X-ALT-DESC;FMTTYPE=text/html:Speaker: Richard Montgomery
(Warwick, IAS)
Title: Finding regul
ar subgraphs
Abstract: Finding regular subgraph
s can be useful. Many results assume a graph is regular or are easier to pr
ove when they are. In 1975, Erdős and Sauer asked for an estimate, for any
constant r, on the maximum number of edges an n-vertex graph can have witho
ut containing an r-regular subgraph (one in which each vertex is in r edges
). The best upper bound on this problem was for a long time one of Pyber fr
om 1985, but the last few years have seen rapid developments, initiated by
Janzer and Sudakov, and we now have an efficient framework to find regular
subgraphs for not only constant r but the whole range of possible values of
r.
I will discuss this framework and its
components, which include algebraic techniques of Alon, Friedland and Kala
i, the recent breakthroughs on the sunflower conjecture, techniques to find
almost-regular subgraphs developed from Pyber’s work, and, crucially, a no
vel random process that efficiently finds a very nearly regular subgraph in
any almost-regular graph.
Joint work with Deb
soumya Chakraborti, Oliver Janzer and Abhishek Methuku.
DTSTAMP:20260827T094721
DTSTART;TZID=America/New_York:20250303T140000
DTEND;TZID=America/New_York:20250303T150000
SEQUENCE:0
TRANSP:OPAQUE
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