Abstract
For two graphs G1, G2, their intersection is given by only keeping the vertices and edges that appear in both. This graph operation is closely related to various intersection graph classes, such as the intersection graphs of axis-aligned rectangles. We are interested in the interplay between the graph intersection operation and χ-boundedness. A hereditary graph class C is χ-bounded if there exists a function upper bounding the chromatic number based on the clique number for each graph in the class. Specifically, we consider for which classes C1 it holds that for any χ-bounded class C2 the class resulting from taking the graph intersection of each pair of graphs from C1 and C2 is χ-bounded. We call such classes χ-guarding. In this talk, I will go over the history of the problem, and discuss some results on characterizing which classes are χ-guarding.
This talk is based on joint work with Aristotelis Chaniotis and Sophie Spirkl.
