The number of connected sparsely edged uniform hypergraphs
Discrete Mathematics
Growth of components in random graphs
Proceedings of the ninth international conference on on Random structures and algorithms
The phase transition in a random hypergraph
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Counting connected graphs inside-out
Journal of Combinatorial Theory Series B
Graphs and Hypergraphs
Counting connected graphs asymptotically
European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
Another proof of Wright's inequalities
Information Processing Letters
Counting connected graphs and hypergraphs via the probabilistic method
Random Structures & Algorithms
Analytic Combinatorics
Multicyclic components in a random graph process
Random Structures & Algorithms
| Hi-index | 5.23 |
Define an @?-component to be a connected b-uniform hypergraph with k edges and k(b-1)-@? vertices. In this paper, we investigate the growth of size and complexity of connected components of a random hypergraph process. We prove that the expected number of creations of @?-components during a random hypergraph process tends to 1 as b is fixed and @? tends to infinity with the total number of vertices n while remaining @?=o(n^1^/^3). We also show that the expected number of vertices that ever belong to an @?-component is ~12^1^/^3@?^1^/^3n^2^/^3(b-1)^-^1^/^3. We prove that the expected number of times hypertrees are swallowed by @?-components is ~2^1^/^33^-^1^/^3n^1^/^3@?^-^1^/^3(b-1)^-^5^/^3. It follows that with high probability the largest @?-component during the process is of size of order O(@?^1^/^3n^2^/^3(b-1)^-^1^/^3). Our results give insight into the size of giant components inside the phase transition of random hypergraphs and generalize previous results about graphs.