Improper choosability and Property B
Ross Kang, Durham University
A fundamental connection between list vertex colourings of graphs and Property B (also known as hypergraph 2-colourability) was already known to Erdös, Rubin and Taylor. We draw similar connections for improper list colourings. This extends results of Kostochka, Alon, and Král' and Sgall for, respectively, multipartite graphs, graphs of large minimum degree, and list assignments with bounded list union.