While the 3-dimensional analogue of the Sperner problem in the plane was known to be PPAD-complete, the complexity of the 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, we settle this open problem proposed by Papadimitriou~\cite{PAP90} fifteen years ago. This also allows us to derive ... more >>>

This paper surveys some of the work that was inspired by Wagner's general technique to prove completeness in the levels of the boolean hierarchy over NP and some related results. In particular, we show that it is DP-complete to decide whether or not a given graph can be colored with ... more >>>

The reachability problem for graphs cannot be described, in the
sense of descriptive complexity theory, using a single first-order
formula. This is true both for directed and undirected graphs, both
in the finite and infinite. However, if we restrict ourselves to
graphs in which a certain graph parameter is fixed ... more >>>