Abstract: The $k$-cut complex of a graph is the simplicial complex whose facets are the complements of vertex sets of size $k$ that induce a disconnected subgraph. This generalizes a graph complex studied by Eagon and Reiner (1998) in their topological extension of Fröberg's theorem on the linear resolution edge ideals (1990). In this talk we will introduce the construction of the cut complex and its connection to commutative algebra and discuss the effect of various graph operations on the shellability of the cut complex.
The first half of the talk will be accessible to beginning graduate students.
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