We consider in this paper two graph orientation problems. The input of both problems is (i) a mixed graph G whose vertex set is V and edge set (resp. arc set) is E (resp. A) and (ii) a set P ⊆ V × V of source-target pairs. The first problem, called S-GO, is a decision problem introduced by Hassin and Megiddo (Linear Algebra and its Applications 114 (1989): 589-602) and defined as follows: is it...

Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and recover signal well, in most cases, we hope the measurement matrix imposed with some special structure. In this paper, based on random graph models, we show that t...

We show that deciding if a mixed graph has a well-balanced orientation is NP -complete.

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

We provide a flexible graph architecture, and an implementation of solvers to some of the most ubiquitous problems in the field of Arc Routing, (The Chinese Postman Problem on undirected, directed, mixed, and windy graphs, as well as the Rural Postman Problem on directed and windy graphs). The project is completed in java, is open source, and is hosted at https://github.com/Olibear/ArcRoutingLi...

We show that a planar graph with girth at least 20t−2 3 has circular chromatic number at most 2+ 1t , improving earlier results. This follows from a general result establishing homomorphisms into special targets for graphs with given girth and given maximum average degree. Other applications concern oriented chromatic number and homomorphisms into mixed graphs with colored edges.

A graph or a directed graph ) , ( E V G ? ) , ( A V G ? f consists of a set V of vertices and a set E of edges, that are simply pairs of vertices, respectively, a set A of arcs that are ordered pairs of vertices. Mixed graphs contain both edges and arcs. Knowledge graphs consist of a set V of unlabeled vertices, called tokens and represented by squares. The knowledge graph is usually a mixed gr...