Related papers: On the Quest for an Acyclic Graph
This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is…
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
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…
We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an…
Clique-width is a graph invariant that has been widely studied in combinatorics and computer science. However, computing the clique-width of a graph is an intricate problem, the exact clique-width is not known even for very small graphs. We…
We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations.…
In order to find Hamiltonian cycle, algorithm should find edges that creates a Hamiltonian cycle. Higher number of edges creates more possibilities to check to solve the problem. Algorithm rests on analysis of original graph and opposite…
Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear…
The family of Directed Acyclic Graphs as well as some related graphs are analyzed with respect to extremal behavior in relation with the family of intersection graphs for families of boxes with transverse intersection.
We study combinatorial indicators related to the characteristic phase transitions associated with coloring a graph optimally and finding a maximum independent set. In particular, we investigate the role of the acyclic orientations of the…
An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on $n$ vertices without directed 2-cycles possesses an acyclic set of size at least $3n/5$. We…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph isomorphism. An edge cut is defined by an edge and the…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…
The asymptotic study of percolation on finite transitive graphs is considered. Several questions and very few answers regarding percolation on finite graphs are presented.
We characterize the equivalence and the weak equivalence of Cayley graphs for a finite group $\C{A}$. Using these characterizations, we find enumeration formulae of the equivalence classes and weak equivalence classes of Cayley graphs. As…
Graph is a useful data structure to model various real life aspects like email communications, co-authorship among researchers, interactions among chemical compounds, and so on. Supporting such real life interactions produce a knowledge…
Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations. Aim of this survey is to describe the main research…