Shang, Yilun (2022) On the tree-depth and tree-width in heterogeneous random graphs. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 98 (9). pp. 78-83. ISSN 0386-2194
|
Text
treetree.pdf - Accepted Version Download (153kB) | Preview |
Abstract
In this note, we investigate the tree-depth and tree-width in a heterogeneous random graph obtained by including each edge eij (i≠j) of a complete graph Kn over n vertices independently with probability pn(eij). When the sequence of edge probabilities satisfies some density assumptions, we show both tree-depth and tree-width are of linear size with high probability. Moreover, we extend the method to random weighted graphs with non-identical edge weights and capture the conditions under which with high probability the weighted tree-depth is bounded by a constant.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | heterogeneous graph, random graph, tree-depth, tree-width |
| Subjects: | G100 Mathematics |
| Department: | Faculties > Engineering and Environment > Computer and Information Sciences |
| Depositing User: | John Coen |
| Date Deposited: | 15 Nov 2022 12:14 |
| Last Modified: | 15 Nov 2022 12:39 |
| URI: | https://nrl.northumbria.ac.uk/id/eprint/50657 |
Actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
