On January 27, 2022, Bo Ning (宁博) from Nankai University, China gave an online talk at the Virtual Discrete Math Colloquium on the number of 3-cycles and 4-cycles in a graph with certain conditions on eigenvalues. The title of his talk was “Substructures and eigenvalues of graphs: Triangles and quadrilaterals“.
Our talk will mainly focus on the relationship between substructures and eigenvalues of graphs. We will briefly survey recent developments on a conjecture of Bollobás and Nikiforov and a classical result of Nosal on triangles. In particular, we shall present counting results for previous spectral theorems on triangles and quadrilaterals. If time allows, we will give a sketch for the proof of one new counting result on triangles.