Creation and Growth of Components in a Random Hypergraph Process

Denote by an -component a connected b-uniform hypergraph with k edges and k(b - 1) - vertices. We prove that the expected number of creations of -component during a random hypergraph process tends to 1 as and b tend to with the total number of vertices n such that = o 3 n b . Under the same conditions, we also show that the expected number of vertices that ever belong to an -component is approximately 121/3 (b-1)1/3 1/3 n2/3 . As an immediate consequence, it follows that with high probability the largest -component during the process is of size O((b - 1)1/3 1/3 n2/3 ). Our results give insight about the size of giant components inside the phase transition of random hypergraphs.

• Type: Conference
• Year: 2006
• Where: COCOON
• Authors: Vlady Ravelomanana, Alphonse Laza Rijamamy
• Keywords: COCOON 2006, Combinatorics, Connected B-uniform Hypergraph, Expected Number, Random Hypergraphs