Events

Title: Uniformly generate graphs with given degrees rapidly

Abstract:

I will survey the research on exact/approximate uniform generation of graphs with prescribed degrees.

Title: On the Strong Nine Dragon Tree Conjecture

Abstract:

Nash-Williams forest covering theorem says that a graph decomposes into $k$ forests if and only if it has fractional arboricity at most $k$. In 2012 Mickeal Montassier, Patrice Ossona de Mendez, Andre Raspaud, and Xuding Zhu  proposed a significant strengthening of Nash-Williams Theorem, called the Strong Nine Dragon Tree Conjecture.

Title: Random Pattern-Avoiding Permutations

Abstract:

A "pattern of length k" is simply a permutation of {1,..,k}.  This pattern is said to be contained in a permutation of {1,...,N} (for N>k) if there is a subsequence of k elements of the (long) permutation that appears in the same relative order as the pattern.

Title: Excluding a ladder

Abstract:

A folklore result says that if a graph does not contain the path of length k as a subgraph, then it has tree-depth at most k.

Title: Network Design $s$-$t$ Effective Resistance

Abstract:

We consider a problem of designing a network with small $s$-$t$ effective resistance. In the problem, we are given an undirected graph $G=(V,E)$, two designated vertices $s,t \in V$, and a budget $k$.

Title: Minimum degree conditions for Hamilton cycles in hypergrahs

Abstract:

A classic result of Dirac states that a graph in which every vertex is connected to at least half of the other vertices contains a Hamilton cycle. How can we generalize Dirac's theorem to hypergraphs?

Title: Moore Graphs

Abstract:

Moore graphs were introduced by Hoffman and Singleton in a fundamental paper. They can be defined as graphs with diameter $d$ and girth $2d+1$.

Title: A generalization of balanced tableaux and matching problems with unique solutions

Abstract:

In this talk, we consider families of finite sets that we call shellable and that have been characterized by Chang and Hirst and Hughes as being the families of sets that admit unique solutions to Hall's matching problem.

Title: List Colouring and Ohba's Conjecture

Abstract:

The question of when the list-chromatic number of a graph G, denoted chi_l(G), equals its chromatic number is fundamental to the theory of list colouring.

Title: The Aggregation Closure is Polyhedral for Packing and Covering Integer Programs

Abstract:

Recently, Bodur, Del Pia, Dey, Molinaro and Pokutta introduced the concept of aggregation cuts for packing and covering integer programs.