The first cycles in an evolving graph
Discrete Mathematics
Practical minimal perfect hash functions for large databases
Communications of the ACM
Improved bounds for covering complete uniform hypergraphs
Information Processing Letters
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
Asymptotic enumeration of sparse graphs with a minimum degree constraint
Journal of Combinatorial Theory Series A
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Counting connected graphs inside-out
Journal of Combinatorial Theory Series B
Cores in random hypergraphs and Boolean formulas
Random Structures & Algorithms
The cores of random hypergraphs with a given degree sequence
Random Structures & Algorithms
Practical perfect hashing in nearly optimal space
Information Systems
Practical perfect hashing in nearly optimal space
Information Systems
Memory efficient sanitization of a deduplicated storage system
FAST'13 Proceedings of the 11th USENIX conference on File and Storage Technologies
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We show that the threshold c"r","k (in terms of the average degree of the graph) for appearance of a k-core in a random r-partite r-uniform hypergraph G"r","n","m is the same as for a random r-uniform hypergraph with cn/r edges without the r-partite restriction, where r,k=2. In both cases, the average degree is c. The case r,k=2 was analyzed in Botelho et al. (2007) [4] but the general case r=3, k=2 is still open. Besides the proof for the general case, we have also provided a simpler proof for the case r,k=2. This problem was provided without a proof (but with strong experimental evidence) in the analysis of the algorithm presented in Botelho et al. (2007) [2]. This algorithm constructs a family of minimal perfect hash functions based on random r-partite r-uniform hypergraphs with an empty k-core subgraph, for k=2. For an input key set S with m keys, the family of minimal perfect hash functions generated by the algorithm can be stored in O(m) bits, where the hidden constant is within a factor of two from the information theoretical lower bound.