Graphs and Matroids Seminar- Bill Kay

Title: Induced Poset Saturation

Abstract: In Graph Theory, we say that a graph G is H saturated if G contains no copy of H as a subgraph, but on addition of any edge G contains a copy of H. For example, any bipartite graph is triangle saturated.
The saturation number of a graph H (denoted sat(n;H)) is the minimum number of edges in an H
saturated graph on n vertices. Saturation serves as a complementary question to extremal numbers and
has been well studied in the case of graphs. Note that for any combinatorial object with a subobject
relation we have a notion of saturation. In this talk, we introduce (induced) saturation in the realm
of Partially Ordered Sets (Posets). Joint work with Michael Ferrara, Lucas Kramer, Ryan R. Martin,
Benjamin Reiniger, Heather C. Smith, Eric Sullivan