Edge ideals of Random Graphs

Abstract: In this talk, we shall look at four properties of edge ideals of Erdos-Renyi random graphs. Namely, we shall consider asymptotics for linear resolution, linear presentation, regularity and unmixedness. These properties have very explicit characterization in terms of graph-theoretic properties such as co-chordality, induced matching number and uniqueness of minimal vertex cover. In this talk, we shall discuss asymptotics for the latter properties of Erdos-Renyi random graphs and their consequences for random edge ideals. Though the random graph theory results will be stated in a self-contained manner, the interest in these results is due to their connection to edge ideals.

Edge ideals and related notions shall be introduced in Arindam Banerjee's talk on November 11th and I shall only recall them very briefly. On the random graph side, I shall assume knowledge of graph theory and basic probability.

The talk is based on a joint work with Arindam Banerjee ; arxiv.org/abs/2007.08869

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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