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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:A bandwidth theorem for approximate decompositions
- Padraig Condon (University of Birmingham)
DTSTART:20180227T150000Z
DTEND:20180227T160000Z
UID:TALK3095AT
URL:/talk/index/3095
DESCRIPTION:We provide a degree condition on a regular $n$-ver
tex graph $G$ which ensures the existence of a nea
r optimal packing of any family $H$ of bounded deg
ree $n$-vertex $k$-chromatic separable graphs into
$G$. In general\, this degree condition is best p
ossible.\n\nHere a graph is separable if it has a
sublinear separator whose removal results in a set
of components of sublinear size. Equivalently\, t
he separability condition can be replaced by that
of having small bandwidth. Thus our result can be
viewed as a version of the bandwidth theorem of B\
\"ottcher\, Schacht and Taraz in the setting of ap
proximate decompositions.\n\nIn particular\, this
yields an approximate version of the tree packing
conjecture in the setting of regular host graphs $
G$ of high degree. Similarly\, our result implies
approximate versions of the Oberwolfach problem\,
the Alspach problem and the existence of resolvabl
e designs in the setting of regular host graphs of
high degree. This is joint work with Jaehoon Kim\
, Daniela K\\"uhn and Deryk Osthus.
LOCATION:Watson LTA
CONTACT:Allan Lo
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