Seminars and Colloquia by Series

TBA by Meike Hatzel

Series
Graph Theory Seminar
Time
Tuesday, October 22, 2024 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Meike Hatzel – National Institute of Informatics

Induction for 4-connected Matroids and Graphs (Xiangqian Joseph Zhou, Wright State University)

Series
Graph Theory Seminar
Time
Tuesday, July 23, 2024 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xiangqian Joseph Zhou – Wright State University –

A matroid $M$ is a pair $(E, \mathcal{I})$ where $E$ is a finite set, called the {\em ground set} of $M$, and $\mathcal{I}$ is a non-empty collection of subsets of $E$, called {\em independent sets} of $M$, such that (1) a subset of an independent set is independent; and (2) if $I$ and $J$ are independent sets with $|I| < |J|$, then exists $x \in J \backslash I$ such that $I \cup \{x\}$ is independent. 

A graph $G$ gives rise to a matroid $M(G)$ where the ground set is $E(G)$ and a subset of $E(G)$ is independent if it spans a forest. Another example is a matroid that comes from a matrix over a field $F$: the ground set $E$ is the set of all columns and a subset of $E$ is independent if it is linearly independent over $F$. 

Tutte's Wheel and Whirl Theorem and Seymour's Splitter Theorem are two well-known inductive tools for proving results for 3-connected graphs and matroids. In this talk, we will give a survey on induction theorems for various versions of 4-connected matroids and graphs.   
 

Conflict-free hypergraph matchings and generalized Ramsey numbers (Emily Heath, Iowa State University)

Series
Graph Theory Seminar
Time
Tuesday, April 16, 2024 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Emily Heath – Iowa State University –

Given graphs G and H and a positive integer q, an (H,q)-coloring of G is an edge-coloring in which each copy of H receives at least q colors. Erdős and Shelah raised the question of determining the minimum number of colors, f(G,H,q), which are required for an (H,q)-coloring of G. Determining f(K_n,K_p,2) for all n and p is equivalent to determining the classical multicolor Ramsey numbers. Recently, Mubayi and Joos introduced the use of a new method for proving upper bounds on these generalized Ramsey numbers; by finding a “conflict-free" matching in an appropriate auxiliary hypergraph, they determined the values of f(K_{n,n},C_4,3) and f(K_n,K_4,5). In this talk, we will show how to generalize their approach to give bounds on the generalized Ramsey numbers for several families of graphs. This is joint work with Deepak Bal, Patrick Bennett, and Shira Zerbib.

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