On Thresholds for the Appearance of 2-cores in Mixed Hypergraphs

Details On Thresholds for the Appearance of 2-cores in Mixed Hypergraphs On Thresholds for the Appearance of 2-cores in Mixed Hypergraphs

2012-04-10

arxiv.org/abs/1204.2131v1

Computer Science

Data Structures and Algorithms

Scientific paper

We study thresholds for the appearance of a 2-core in random hypergraphs that are a mixture of a constant number of random uniform hypergraphs each with a linear number of edges but with different edge sizes. For the case of two overlapping hypergraphs we give a solution for the optimal (expected) number of edges of each size such that the 2-core threshold for the resulting mixed hypergraph is maximized. We show that for adequate edge sizes this threshold exceeds the maximum 2-core threshold for any random uniform hypergraph, which can be used to improve the space utilization of several data structures that rely on this parameter.

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