This book is a revised version of my 2005 thesis [71] for the degree of Doctor of Philosophy
at the Royal Institute of Technology (KTH) in Stockholm. The whole idea of writing a …

To every directed graph G one can associate a complex Δ (G) consisting of directed
subforests. This construction, suggested to us by R. Stanley, is especially important in the …

This monograph studies the interplay between various algebraic, geometric and
combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and …

Black box techniques¹2 are enabling exact linear algebra computations of a scale well
beyond anything previously possible. The development of new and interesting algorithms …

We present a new algorithm to compute the Integer Smith normal form of large sparse
matrices. We reduce the computation of the Smith form to independent, and therefore …

We survey results and techniques in the topological study of simplicial complexes of (di-,
multi-, hyper-) graphs whose node degrees are bounded from above. These complexes …

Topological properties of the matching complex were first studied by Bouc in connection with
Quillen complexes, and topological properties of the chessboard complex were first studied …

Multipath cohomology is a cohomology theory for directed graphs, which is defined using
the path poset. The aim of this paper is to investigate combinatorial properties of path posets …

It is shown that the neighborhood complexes of a family of vertex critical subgraphs of
Kneser graphs—the stable Kneser graphs introduced by L. Schrijver—are spheres up to …

A multipath in a directed graph is a disjoint union of paths. The multipath complex of a
directed graph G \ttG is the simplicial complex whose faces are the multipaths of G \ttG. We …