Related papers: Closed orders and closed graphs

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.

The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…

Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…

We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed…

Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

We study topological properties of the graph topology.

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.

Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of…

The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval…

A consequence of Ore's classic theorem characterizing the maximal graphs with given order and diameter is a determination of the largest such graphs. We give a very short and simple proof of this smaller result, based on a well-known…

The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…

In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…

We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…

We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.

We describe the missing class of the hierarchy of mixed unit interval graphs, generated by the intersection graphs of closed, open and one type of half-open intervals of the real line. This class lies strictly between unit interval graphs…

Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.

We study the homotopy theory of diagrams of chain complexes over a field indexed by a finite poset, and show that it can be completely described in terms of appropriate diagrams of graded vector spaces.

There is a well-documented research programme on graph operators which addresses questions such as `Which graphs appear as images of graphs?'; `Which graphs are fixed under the operator?'; `What happens if the operator is iterated?' In this…