Speaker: Daniel Paulusma

Title: Clique-width and Graph Colouring for Hereditary Graph Classes

Abstract: Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class GC is bounded by a constant, a wide range of problems that are NP-complete in general can be shown to be polynomial-time solvable for GC. For this reason, the boundedness or unboundedness of clique-width has been investigated and determined for many graph classes. We survey results on clique-width for hereditary graph classes, which are the graph classes closed under vertex deletion. We also discuss algorithmic consequences of these results, in particular for Graph Colouring. We will point out relevant open problems throughout the talk.