Martin Koutecký Solving hard problems on Neighborhood Diversity

The topic of this thesis is the complexity of some hard problems on graphs when parametrized by neighborhood diversity, a recently introduced graph parameter capturing some structural graph properties, and possibly by other related parameters. The student will survey relevant interesting problems and results (e.g., problems that are hard when parametrized by treewidth or which fall into a cathegory not investigated yet with regards to the new parameters), parameters (such as neighborhood diversity, finite type etc.) and useful techniques (e.g., Lenstra’s integer linear programming algorithm in fixed dimension). The student will then try to tackle some of the open problems.