From f71d455933d4f86845b1069af36f74129ce4b442 Mon Sep 17 00:00:00 2001 From: Munsee Date: Mon, 26 Aug 2024 15:13:18 +0100 Subject: [PATCH] added another abstract --- abstracts/weiss.md | 16 ++++++++++++++++ program.md | 2 +- 2 files changed, 17 insertions(+), 1 deletion(-) create mode 100644 abstracts/weiss.md diff --git a/abstracts/weiss.md b/abstracts/weiss.md new file mode 100644 index 0000000..b5e9b58 --- /dev/null +++ b/abstracts/weiss.md @@ -0,0 +1,16 @@ +--- +layout: default +permalink: /abstracts/weiss +--- + +## Meike Weiß + +### Embedding Cubic Graphs on Simplicial Surfaces + +We study simplicial surfaces, which describe the incidence relations of triangulated surfaces. + +By considering only the incidence between faces and edges, we can define a cubic graph associated to a simplicial surface, called the face graph. Several properties of simplicial surfaces can be transferred to properties of their face graphs, where e.g. 3-connectivity plays a particular role. + +The more interesting and challenging direction is to investigate, for a given cubic graph $G$, whether there exists a simplicial surface which has $G$ as its face graph. We shall see in this talk that computing such a simplicial surface is equivalent to computing a cycle double cover of the graph. Moreover, we know from Whitney's embedding theorem that 3-connected cubic planar graphs are uniquely embeddable on the sphere. + +This embedding can be translated into a unique embedding of the graph on the simplicial sphere. In addition, 3-connected cubic planar graphs can also be embedded on simplicial surfaces of higher genus. We characterise the properties a face graph $G$ of a simplicial sphere must have to guarantee the existence of a simplicial surface with non-negative Euler characteristic which also has $G$ as its face graph. Furthermore, I show some computational results computed with GAP. \ No newline at end of file diff --git a/program.md b/program.md index 0d1866d..2a100ca 100644 --- a/program.md +++ b/program.md @@ -50,7 +50,7 @@ This schedule is subject to change. - 11:00 Work session - 12:30 *Lunch break* - 13:30 Work session - - 15:00 Talk: *"Embedding Cubic Graphs on Simplicial Surfaces"* (Meike Weiß) + - 15:00 Talk: *"Embedding Cubic Graphs on Simplicial Surfaces"* (Meike Weiß)([abstract]({{ site.baseurl }}/abstracts/weiss)) - 15:30 Work session - 16:45 Stand-up Meeting: Results from work sessions