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CATEGORIES:Combinatorics Seminar
SUMMARY:Hamilton spheres in 3-uniform hypergraphs - John H
aslegrave (University of Warwick)
DTSTART;TZID=Europe/London:20180201T143000
DTEND;TZID=Europe/London:20180201T153000
UID:TALK96853AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/96853
DESCRIPTION:Dirac's theorem states that any n-vertex graph wit
h minimum degree at least n/2 contains a Hamilton
cycle. Rödl\, Rucinski and Szemerédi showed that a
symptotically the same bound gives a tight Hamilto
n cycle in any k-uniform hypergraph\, where in thi
s case "minimum degree" is interpreted as the mini
mum codegree\, i.e. the minimum over all (k-1)-set
s of the number of ways to extend that set to an e
dge. The notion of a tight cycle can be generalise
d to an l-cycle for any l at most k\, and correspo
nding results for l-cycles were proved independent
ly by Keevash\, Kühn\, Mycroft and Osthus and by H
àn and Schacht\, and extended to the full range of
l by Kühn\, Mycroft and Osthus. However\, l-cycle
s are essentially one-dimensional structures. A na
tural topological generalisation of Hamilton cycle
s in graphs to higher-dimensional dtructures is to
ask for a spanning triangulation of a sphere in a
3-uniform hypergraph. We give an asymptotic Dirac
-type result for this problem. Joint work with Age
los Georgakopoulos\, Richard Montgomery and Bharga
v Narayanan.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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