Name
Abstract | ||
|---|---|---|
Given integers k, j with 1 < j < k - 1, we consider the length of the longest j-tight path in the binomial random k-uniform hypergraph Hk(n, p). We show that this length undergoes a phase transition from logarithmic length to linear and determine the critical threshold, as well as proving upper and lower bounds on the length in the subcritical and supercritical ranges. In particular, for the supercritical case we introduce the Pathfinder algorithm, a depth-first search algorithm which discovers j-tight paths in a k-uniform hypergraph. We prove that, in the supercritical case, with high probability this algorithm will find a long j-tight path. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/20M1345712 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
random hypergraphs, paths, phase transition, search algorithm | Journal | 35 |
Issue | ISSN | Citations |
4 | 0895-4801 | 0 |
PageRank | References | Authors |
0.34 | 0 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Oliver Cooley | 1 | 39 | 9.15 |
| Garbe Frederik | 2 | 0 | 0.34 |
| Hng Eng Keat | 3 | 0 | 0.34 |
| Mihyun Kang | 4 | 163 | 29.18 |
| Sanhueza-Matamala Nicolás | 5 | 0 | 0.34 |
| Zalla Julian | 6 | 0 | 0.34 |