Related papers: Transitive closure and transitive reduction in bid…
A new approach to find all the transitive orientations for a comparability graph (finite or infinite) is presented. This approach is based on the link between the notion of ``strong'' partitive set and the forcing theory (notions of…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…
An orientation of a graph is semi-transitive if it contains no directed cycles and has no shortcuts. An undirected graph is semi-transitive if it can be oriented in a semi-transitive manner. The class of semi-transitive graphs includes…
In many complex networks the vertices are ordered in time, and edges represent causal connections. We propose methods of analysing such directed acyclic graphs taking into account the constraints of causality and highlighting the causal…
A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.
Recently, bidirected graphs have received increasing attention from the graph theory community with both structural and algorithmic results. Bidirected graphs are a generalization of directed graphs, consisting of an undirected graph…
A transitive graph is 2-dimensional if it can be represented as the intersection of two linear orders. Such representations make answering of reachability queries trivial, and allow many problems that are NP-hard on arbitrary graphs to be…
We develop a new framework for analysing finite connected, oriented graphs of valency 4, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of "basic" graphs…
We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the reals. In particular, we give a characterization of the real…
\emph{Bidirected graphs} (a sort of nonstandard graphs introduced by Edmonds and Johnson) provide a natural generalization to the notions of directed and undirected graphs. By a \emph{weakly (node- or edge-) acyclic} bidirected graph we…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
This paper is the first from serial papers that provide constructive characterizations for classes of bidirected graphs known as radials and semiradials. In this paper, we provide constructive characterizations for five principle classes of…
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…
We show that the categories of directed and undirected reflexive graphs carry exactly two (up to isomorphism) biclosed monoidal structures.
We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…
We study transitivity properties of graphs with more than one end. We completely classify the distance-transitive such graphs and, for all $k \geq 3$, the $k$-CS-transitive such graphs.
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
In this short note we make a few remarks on a class of generalized incidence matrices whose matroids do not depend on the orientation of the underlying graph and natural commutative algebras associated to such matrices.
We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns closely with the notions of tree-depth and shrub-depth of graphs…