On the independence and chromatic numbers of random regular graphs
Journal of Combinatorial Theory Series B
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
Asymptotics for dependent sums of random vectors
Random Structures & Algorithms
Random Regular Graphs of Non-Constant Degree: Connectivity and Hamiltonicity
Combinatorics, Probability and Computing
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
A phase transition for avoiding a giant component
Random Structures & Algorithms
The k-orientability thresholds for Gn, p
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The k-core and branching processes
Combinatorics, Probability and Computing
The probability that a random multigraph is simple
Combinatorics, Probability and Computing
Tight thresholds for cuckoo hashing via XORSAT
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Orientability of random hypergraphs and the power of multiple choices
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Hamilton Cycles in Random Graphs with a Fixed Degree Sequence
SIAM Journal on Discrete Mathematics
The multiple-orientability thresholds for random hypergraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The rigidity transition in random graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Cores of random r-partite hypergraphs
Information Processing Letters
Sharp load thresholds for cuckoo hashing
Random Structures & Algorithms
Maximum matchings in random bipartite graphs and the space utilization of Cuckoo Hash tables
Random Structures & Algorithms
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We study random r-uniform n vertex hypergraphs with fixed degree sequence d = (d1…,dn), maximum degree &Dgr; = o(n1/24) and total degree &thgr;n, where &thgr; is bounded. We give the size, number of edges and degree sequence of the &kgr; ≥ 2) up to a whp error of O(n2/3 &Dgr;4/3 log n). In the case of graphs (r = 2) we give further structural details such as the number of tree components and, for the case of smooth degree sequences, the size of the mantle. We give various examples, such as the cores of r-uniform hypergraphs with a near Poisson degree sequence, and an improved upper bound for the first linear dependence among the columns in the independent column model of random Boolean matrices. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 25, 2004