Uniformization properties and graph edge colourings

יום ב', 11/02/2019 - 13:00

Sierpinski's now classical result states that there is an edge 2-colouring of the complete graph on aleph1 vertices so that there are no uncountable monochromatic subgraphs. In the 1970s, Erdos, Galvin and Hajnal asked what other graphs with large chromatic number admit similar edge colourings i.e., with no 'large' monochromatic subgraphs. We plan to review some recent advances on this problem and in particular, connect the question to Shelah's ladder system uniformization theory.