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Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given ‘far away’ observations. Several theoretical results (a...
We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. ...
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sp...
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS
A SEQUENTIAL IMPORTANCE SAMPLING ALGORITHM FOR GENERATING RANDOM GRAPHS WITH PRESCRIBED DEGREES。
RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE。
For a graph $G$, denote by $t(G)$ (resp. $b(G)$) the maximum size of a triangle-free (resp. bipartite) subgraph of $G$. Of course $t(G) \geq b(G)$ for any $G$, and a classic result of Mantel from 1907...
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
A path in an edge-colored graph is called a rainbow path if the edges on it have distinct colors. For k  1, the rainbow-k-connectivity of a graph G, denoted by rck(G), is the minimum number of colors...
Abstract: We describe and analyse a simple greedy algorithm \2G\ that finds a good 2-matching $M$ in the random graph $G=G_{n,cn}^{\d\geq 3}$ when $c\geq 15$. A 2-matching is a spanning subgraph of ma...
A path in an edge-colored graph is called a rainbow path if all edges on it have pairwise distinct colors. For k ≥ 1, the rainbow-k-connectivity of a graph G, denoted rck(G), is the minimum number o...
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is fu...
In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest ...
In this article, we develop a general method to obtain local limit theorems from distributional limit theorems. Our results use probabilistic arguments and yield explicit bounds on the quality of app...

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