Results 31 to 40 of about 2,487,806 (297)
Physical Review Letters, 2002 We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable.
R. MULET +3 more
openaire +6 more sources
On the Vertex-Connectivity of an Uncertain Random Graph
IEEE Access, 2020 In many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which ...
Hao Li, Xin Gao
doaj +1 more source
The rank of random graphs [PDF]
Random Structures & Algorithms, 2008 AbstractWe show that almost surely the rank of the adjacency matrix of the Erdős‐Rényi random graph G(n,p) equals the number of nonisolated vertices for any c ln n/n ≤ p ≤ 1/2, where c is an arbitrary positive constant larger than 1/2. In particular, the adjacency matrix of the giant component (a.s.) has full rank in this range.
Kevin P. Costello, Van H. Vu
openaire +4 more sources
Taylor’s power law for the
Modern Stochastics: Theory and Applications, 2019 Taylor’s power law states that the variance function decays as a power law. It is observed for population densities of species in ecology. For random networks another power law, that is, the power law degree distribution is widely studied.
István Fazekas +2 more
doaj +1 more source
The number of planar graphs and properties of random planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.
Omer Gimenez, Marc Noy
doaj +1 more source
A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions
Mathematics, 2021 A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles.
István Fazekas, Attila Barta
doaj +1 more source
Combinatorica, 1988 We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class.
Chung, F. R. K. +2 more
openaire +4 more sources
Asymptotic Behavior of the Edge Metric Dimension of the Random Graph
Discussiones Mathematicae Graph Theory, 2021 Given a simple connected graph G(V,E), the edge metric dimension, denoted edim(G), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S.
Zubrilina Nina
doaj +1 more source
Random rectangular graphs [PDF]
Physical Review E, 2015 A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides ...
Estrada, Ernesto, Sheerin, Matthew
openaire +5 more sources
On hamiltonicity of uniform random intersection graphs
Lietuvos Matematikos Rinkinys, 2010 We give a sufficient condition for the hamiltonicity of the uniform random intersection graph G{n,m,d}. It is a graph on n vertices, where each vertex is assigned d keys drawn independently at random from a given set of m keys, and where any two vertices
Mindaugas Bloznelis +1 more
doaj +1 more source