Combinatorics Seminar
Usual meeting time is Monday 3:20-4:20 in LeConte 312. If you want to
give a talk, contact Laszlo Szekely.
- !!!CANCELLED!!!April 17, Lincoln Lu, "On 3-chromatic non-uniform hypergraphs"
Abstract:
For a non-uniform hypergraph H, let f(H) be the number of
red edges if each vertex is colored in red and blue with equal
probability independently. A hypergraph is said to have property B
if there is a red-blue vertex-coloring of H with no monochromatic edge.
Here we prove that every hypergraph H with minimum edge cardinality r
and f(H)> c ln r / ln ln r must have Property B.
- April 3, Peter Erdos, Renyi Institute of the Hungarian Academy of Sciences
"Splitting property in finite and infinite posets"
(joint work with Lajos Soukup)
- March 13, Laszlo Szekely "Biplanar crossing numbers - using the
probabilistic method" - continued
- February 27, Laszlo Szekely "Biplanar crossing numbers - using the
probabilistic method"
- February 20, Yiting Yang "On a Randic index conjecture"
Abstract:
The Radic index $R(G)$ of a graph G is defined as the sum of the weights
${d(u)d(v)}^{-1/2}$ over all edges uv of G, where d(u) is the degree of vertex
u. Delorme et al. proposed the following conjecture on the Randic index:
If G is a graph of order n and $\delta(G)\geq\delta\geq 1$, then
$$R(G)\geq\frac{\delta(n-\delta)}{\sqrt{\delta(n-1)}}+
\frac{\delta(\delta-1)}{2}\frac{1}{n-1}$$,
where $\delta(G)$ is the minimum degree of $G$.
We will show that the conjecture is not true when $\delta>\frac{n}{2}$,
$n\neq 2$ (mod 4) and prove the corrected conjecture for the graphs with only
two kind of degrees.
- February 6, Lincoln Lu "Entropy"
Abstract:
The talk will be an introduction to entropy,
motivated by applications to combinatorics.
- Januar 23, Laszlo Szekely "Variational distance of phylogenetic
model trees"
Abstract:
A widely-studied model for generating sequences is to "evolve" them on a
tree according to a symmetric Markov process.
Model trees tend to be maximally "far apart" in terms of variational distance.
Yet, almost paradoxically, tree reconstruction is successful for sequences
that are short enough that the sample is also likely to have near-maximal
variational distance from the model tree. This is a joint work with Mike Steel.
- Combinatorics seminar in 2005