We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time algorithm for finding an optimal solution. For the latter problem, we give a linear-time algorithm for finding a feasible solution whose size is equal to the obvious...

Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) model theory. Therefore, the concept of nowhere density seems to capture a natural property of g...

Tutte conjectured that every 4-edge connected graph admits a nowhere-zero Z3-flow and Jaeger, Linial, Payan and Tarsi conjectured that every 5-edge connected graph is Z3-connected. In this paper, we characterize the triangularly connected graphs G that are Γ-connected for any Abelian group Γ with |Γ| ≥ 3. Therefore, these two conjectures are verified for the family of triangularly connected gra...

We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to Rademacher theorem for graphs.

We present a new family of graphical models that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them can be seen as the result of marginalizing out some nodes in an AMP chain graph. However, MAMP chain graphs do not only subsume AMP chain graphs but also regression chain graphs. We describe global and local Markov pr...

We define binet matrices, which furnish a direct generalization of totally unimodular network matrices and arise from the node-edge incidence matrices of bidirected graphs in the same way as the network matrices do from directed graphs. We develop the necessary theory, give binet representations for interesting sets of matrices, characterize totally unimodular binet matrices and discuss the rec...