相关论文: Exact expectations for random graphs and assignmen…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.
A "book" with k pages consists of a straight line (the "spine") and k half-planes (the "pages"), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine,…
The binomial random bipartite graph $G(n,n,p)$ is the random graph formed by taking two partition classes of size $n$ and including each edge between them independently with probability $p$. It is known that this model exhibits a similar…
We study the earliest arrival problem in road networks with static time-dependent functions as arc weights. We propose and evaluate the following simple algorithm: (1) average the travel time in k time windows, (2) compute a shortest…
We obtain an exact formula for the probability that a uniformly random spanning tree of the $2$-by-$n$ square grid is ``balanced'' in the sense that it has an edge whose removal partitions its vertices into two sets of equal size. We…
We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the factors except one or two are small. The resulting asymptotic behaviour is seen to…
We study the k-core of a random (multi)graph on n vertices with a given degree sequence. We let n tend to infinity. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
By means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on $n$ vertices chosen uniformly at random satisfies an estimate of the form $s \varrho^{-n} (1+o(1))$, where…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdi\`ere-type parameters. Let $G(v,p)$ denote the usual…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching…
We discuss the expected minimum cost of rainbow spanning trees and Hamilton cycles in randomly edge colored random graphs.
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs with this property for all subgraphs with…
We study the minimum spanning arborescence problem on the complete digraph $\vec{K}_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent uniform random variable $U^\alpha$ where $\alpha\leq 1$ and $U$ is…
We consider random-access networks with nodes representing transmitter-receiver pairs whose signals interfere with each other depending on their vicinity. Data packets arrive at the nodes over time and form queues. The nodes can be either…