Title: A recursive spectral bound for independenceSpeaker: Bogdan Nica Affiliation: Indiana University-Purdue University Indianapolis Location: Contact Sabrina Lato for Zoom link
Abstract: We discuss an upper bound for the independence number of a graph, in the spirit of the well-known Hoffman bound. Our bound involves the largest Laplacian eigenvalue of the graph; more surprisingly, it also involves the independence number of a certain induced graph. We illustrate the bound on several examples.
Title: k-Connectedness and k-Factors in the Semi-Random Graph ProcessSpeaker: Hidde Koerts Affiliation: University of Waterloo Location: MC 6029
Abstract: The semi-random graph process is a single player graph game where the player is initially presented an edgeless graph with n vertices. In each round, the player is offered a vertex u uniformly at random and subsequently chooses a second vertex v deterministically according to some strategy, and adds edge uv to the graph. The objective for the player is then to ensure that the graph fulfils some specified property as fast as possible.