On Wednesday the 19th of January 2017, at 10:15 in Takustr. 9, SR 046
William T. Trotter (Georgia Institute of Technology)
will give a talk on
Dimension and Cut Vertices.
When: On Thursday 19.01.2017, at 10:15.
Where: At Takustr. 9 , 14195 Berlin, in room SR 046 .
Motivated by quite recent research involving the relationship
between the dimension of a poset and graph theoretic properties
of its cover graph, we show that for every $d\ge 1$, if $P$ is
a poset and the dimension of a subposet $B$ of $P$ is at most~$d$
whenever the cover graph of $B$ is a block of the cover graph of $P$,
then the dimension of $P$ is at most $d+2$. We also construct
examples which show that this inequality is best possible.
We consider the proof of the upper bound to be fairly elegant
and relatively compact. However, we know of no simple proof for
the lower bound, and our argument requires a powerful tool known
as the Product Ramsey Theorem. As a consequence, our constructions
involve posets of enormous size.
Joint research with Bartosz Walczak and Ruidong Wang