Partition universality of G(n,p) for degenerate graphs

The r-​colour size-​Ramsey number of a graph G is the minimum number of edges of a graph H such that any r-​colouring of the edges of H has a monochromatic G-​copy. Random graphs play an important role in the study of size-​Ramsey numbers. Using random graphs, we establish a new bound on the size-​Ramsey number of D-​degenerate graphs with bounded maximum degree.

In the talk I will summarise what is known about size-​Ramsey numbers, explain the connection to random graphs and their so-​called partition universality, and outline which methods we use in our proof.

Based on joint work with Peter Allen.