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* Princeton Discrete Math Seminar *
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Speaker: Rose McCarty (Waterloo)
Thursday 22nd April, 3:00 via Zoom.
Title: Vertex-minors and immersions
The vertex-minors of a graph G are the graphs that can be obtained from G using
two operations:
1) deleting a vertex and
2) replacing the induced subgraph on the neighborhood of a vertex by its
complement.
This second operation gives a good deal of freedom, and we conjecture that there
is a nice structural description of graph classes that exclude a vertex-minor.
We discuss how to understand the ''local structure'' via a connection with
immersion minors. This is perhaps surprising since classes that exclude a
vertex-minor are usually dense (i.e. contain all bicliques), while classes that
exclude an immersion minor must be sparse.
This is joint work with Jim Geelen and Paul Wollan.
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Next week: summer
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