# Online Talk: O-joung Kwon

Tuesday, March 22, 5pm ET (*9pm* GMT, *10am* Wed NZDT)
O-joung Kwon, Hanyang University
Reduced bandwidth: a qualitative strengthening of twin-width in minor-closed classes (and beyond)

##### In a reduction sequence of a graph, vertices are successively identified until the graph has one vertex. At each step, when identifying $u$ and $v$, each edge incident to exactly one of $u$ and $v$ is coloured red. Bonnet, Kim, Thomassé and Watrigant [J. ACM 2022] defined the twin-width of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has maximum degree at most $k$. For any graph parameter $f$, we define the reduced $f$ of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has $f$ at most $k$. Our focus is on graph classes with bounded reduced bandwidth, which implies and is stronger than bounded twin-width (reduced maximum degree). We show that every proper minor-closed class has bounded reduced bandwidth, which is qualitatively stronger than an analogous result of Bonnet et al. for bounded twin-width. In many instances, we also make quantitative improvements. Furthermore, we separate twin-width and reduced bandwidth by showing that any infinite class of expanders excluding a fixed complete bipartite subgraph has unbounded reduced bandwidth, while there are bounded-degree expanders with twin-width at most 6. This is joint work with Édouard Bonnet and David Wood.

Tuesday, March 15, 3pm ET (*7pm* GMT, *8am* Wed NZDT)
On packing dijoins in digraphs and weighted digraphs

# Online Talk: Sang-il Oum

Tuesday, March 8, **4pm ET** (9pm GMT, 10am Wed NZDT)
Sang-il Oum, Institute for Basic Science / KAIST
Obstructions for matroids of path-width at most $k$ and graphs of linear rank-width at most $k$

# Online Talk: Louis Esperet

Tuesday, March 1, 11am ET (4pm GMT, 5am Wed NZDT)
Louis Esperet, G-SCOP Laboratory (CNRS, Grenoble)
Packing and covering balls in planar graphs