Related papers: Classifying grounded intersection graphs via order…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
An \emph{asteroidal triple} is a set of three independent vertices in a graph such that any two vertices in the set are connected by a path which avoids the neighbourhood of the third. A classical result by Lekkerkerker and Boland \cite{6}…
The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…
A metric basis in a graph $G$ is a smallest possible set $S$ of vertices of $G$, with the property that any two vertices of $G$ are uniquely recognized by using a vector of distances to the vertices in $S$. A strong metric basis is a…
Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes…
The speed of a class of graphs counts the number of graphs on the vertex set $\lbrace 1,\dots, n\rbrace$ inside the class as a function of $n$. In this paper, we investigate this function for many classes of graphs that naturally arise in…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
Strongly chordal graphs are a subclass of chordal graphs. Farber also established a number of different characterisations for this class of graphs. These include an intersection graph characterisation that is analogous to a similar…
A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. Following analogous studies in the literature related to independent sets, dominating sets, and total dominating sets, we study in this…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
A graph is odd if all of its vertices have odd degrees. In particular, an odd spanning tree in a connected graph is a spanning tree in which all vertices have odd degrees. In this paper we establish a unified technique to enumerate odd…
A mixed graph is a graph with some directed edges and some undirected edges. We introduce the notion of mixed matroids as a generalization of mixed graphs. A mixed matroid can be viewed as an oriented matroid in which the signs over a fixed…
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
Let $B=(X,Y,E)$ be a bipartite graph. A half-square of $B$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. Every planar graph is a half-square of a planar bipartite…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
A blocking quadruple (BQ) is a quadruple of vertices of a graph such that any two vertices of the quadruple either miss (have no neighbours on) some path connecting the remaining two vertices of the quadruple, or are connected by some path…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…