Seminar
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| Location: | SLMath: Online/Virtual, Baker Board Room |
Models of global structure
Various graph properties can exist for "local" or for "global" reasons. For example, some graphs have high chromatic number because they contain a large clique, so their high chromatic number is witnessed locally. But other graphs have high chromatic number and high girth, and in these graphs, high chromatic number is witnessed only globally.
These two examples indicate that high chromatic number can appear as either a local or a global feature of a graph. With good definitions of "local" and "global," we could ask for a local-global analysis of any graph property: given a graph exhibiting a certain property, is this property a local or a global feature of this graph?
In this talk, I will discuss a recent framework for understanding local vs global structure of graphs, focusing on decompositions that represent global structure. The talk will include recent results and also ideas, questions, and open problems related to the implications of this model of global structure. My goal is to foster discussion and exchange of ideas during this talk, so feel free to come ready to share your thoughts and reactions!
This talk is based on joint work with Reinhard Diestel and Paul Knappe.