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Thu, May 23, 2024

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Math Seminar Series  (Conferences / Seminars / Lectures)

Combinatorics and Graph Theory

Ira Gessel, Brandeis University, will be speaking.

The topic is "Counting graphs with neighborhood restrictions."

Contact Bruce E Sagan ( for more information.

A graph is called point-determining (or mating type) if no two vertices have the same neighborhood. An arbitrary graph can be reduced to a point-determining graph by contracting each set of vertices with the same neighborhood to a single vertex, and this decomposition enables us to give a simple exponential generating function for counting point-determining graphs, as accomplished by Ronald Read in 1989. In this talk we will discuss a closely related problem: counting graphs in which no two vertices have complementary neighborhoods. The decomposition approach does not work here. Instead we apply inclusion-exclusion, similarly to its use in rook theory, to obtain a simple exponential generating function for these graphs. We also discuss how this application of inclusion-exclusion is related to Möbius inversion, and how it can be applied to some related problems.

more information...

Location: Online via Zoom [map]
Price: free
Sponsor: Department of Mathematics
Contact: Department of Mathematics
phone pic (517) 353-0844