Related papers: RMF accessibility percolation on oriented graphs
In a previous paper, we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph, and showed that this triangle condition implies that the…
Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…
In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem consists in…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
Following Bradonji\'c and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the $2$-dimensional torus. In this model, the expected number of vertices of the graph is $n$, and the expected degree of a…
We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are…
Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the weight of $f$ is $w(f)=\sum_{u\in V}f(u)$ which is just the total number of pebbles…
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…
We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\kappa}_v$ which takes the value $j\in \{0,1,2,3\}$ with probability…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
First passage percolation with recovery is a process aimed at modeling the spread of epidemics. On a graph $G$ place a red particle at a reference vertex $o$ and colorless particles (seeds) at all other vertices. The red particle starts…
The Hamming torus of dimension $d$ is the graph with vertices $\{1,\dots,n\}^d$ and an edge between any two vertices that differ in a single coordinate. Bootstrap percolation with threshold $\theta$ starts with a random set of open…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
We introduce a model of percolation induced by disorder, where an initially homogeneous network with links of equal weight is disordered by the introduction of heterogeneous weights for the links. We consider a pair of nodes i and j to be…
Given a hypergraph $\mathcal{H}$, the $\mathcal{H}$-bootstrap process starts with an initial set of infected vertices of $\mathcal{H}$ and, at each step, a healthy vertex $v$ becomes infected if there exists a hyperedge of $\mathcal{H}$ in…
Rigidity Percolation with g degrees of freedom per site is analyzed on randomly diluted Erdos-Renyi graphs with average connectivity gamma, in the presence of a field h. In the (gamma,h) plane, the rigid and flexible phases are separated by…
The theme of this paper is the analysis of bootstrap percolation processes on random graphs generated by preferential attachment. This is a class of infection processes where vertices have two states: they are either infected or…
We compare level-set percolation for Gaussian free fields (GFFs) defined on a rectangular subset of $\delta \mathbb{Z}^2$ to level-set percolation for GFFs defined on the corresponding metric graph as the mesh size $\delta$ goes to 0. In…
The adaptive evolution of a population under the influence of mutation and selection is strongly influenced by the structure of the underlying fitness landscape, which encodes the interactions between mutations at different genetic loci.…