Path-driven orientation of mixed graphs

Unilateral Orientation of Mixed Graphs

A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M = (V,A,E) with arc-set A and edgeset E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally...

Forced Orientation of Graphs

On the oriented perfect path double cover conjecture

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

On the Complexity of two Problems on Orientations of Mixed Graphs

Interactions between biomolecules within the cell can be modeled by biological networks, i.e. graphs whose vertices are the biomolecules (proteins, genes, metabolites etc.) and whose edges represent their functional relationships. Depending on their nature, the interactions can be undirected (e.g. protein-protein interactions, PPIs) or directed (e.g. protein-DNA interactions, PDIs). A physical ...

Steiner Forest Orientation Problems

We consider connectivity problems with orientation constraints. Given a directed graph D and a collection of ordered node pairs P let P [D] = {(u, v) ∈ P : D contains a uv-path}. In the Steiner Forest Orientation problem we are given an undirected graph G = (V,E) with edge-costs and a set P ⊆ V × V of ordered node pairs. The goal is to find a minimum-cost subgraph H of G and an orientation D of...