Monday, January 18, 3pm ET (8pm GMT, 9am Tue NZDT)
Kazuhiro Nomoto, University of Waterloo
$I_t$-free, triangle-free binary matroids
For any integer $t \geq 1$, we say that a simple binary matroid is $I_t$-free if no rank-$t$ flats are independent. It is triangle-free if it has no circuit of size $3$. In this talk, we discuss a few problems regarding simple $I_t$-free, triangle-free binary matroids, with some partial results.
Joint work with Peter Nelson.
As things can get hard to find on the blog, I’ll be updating this post with links to our content from this year, after the fact. For now, we just had our first online talk last Monday 🙂 – there’ll be more content to look out for soon!
For upcoming talks and a permanent link to this post, see the “Talks
Past online talks:
Monday, January 11, 3pm ET (8pm GMT, 9am Tue NZDT)
Stephan Kreutzer, TU Berlin
A tangle in a graph $G$ is a consistent orientation of all low-order separations of $G$.
In this way, tangles define the “highly connected” pieces of the graph.
Robertson and Seymour introduced the concept of tangles as part of their graph minor series and proved that the maximal tangles in a graph form a tree structure. More formally, every graph has a tree-decomposition whose pieces correspond to its maximal tangles. This tangle decomposition theorem is one of the essential steps in their proof of the graph minor theorem and has also found many other applications.
Recently, we defined “directed tangles”, the analogue of tangles for digraphs, and showed that again every digraph can be decomposed into a tree of its maximal tangles.
In this talk I will introduce directed tangles and present a proof of the main directed tangle decomposition theorem. I will also focus on the differences between the directed and undirected case and sketch potential applications of the directed tangle decomposition theorem.
The talk is based on joint with with Archontia Giannopoulou, Ken-ichi Kawarabayashi, and O-Joung Kwon.
This post contains a list of our content from 2020 for easy access. The online talks will resume on January 11 with a talk by Stephan Kreutzer from TU Berlin. Thanks to everyone who participated in the open problems session – it was great seeing the problems and seeing you there! Have a good winter break.
Online talks [also see the Youtube playlist]: