| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Monash Univ, Melbourne, Vic - Australia
[2] Univ Nebraska, Lincoln, NE - USA
[3] Univ Fed ABC, Ctr Math Comp & Cognit, Santo Andre - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | RANDOM STRUCTURES & ALGORITHMS; v. 52, n. 3, p. 495-535, MAY 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
We study the arboricity A and the maximum number T of edge-disjoint spanning trees of the classical random graph g(n,p). For all p(n) is an element of {[}0,1], we show that, with high probability, T is precisely the minimum delta and {[}m/ (n - 1)], where delta is the minimum degree of the graph and m denotes the number of edges. Moreover, we explicitly determine a sharp threshold value for p such that the following holds. above this threshold, T equals floor {[}m/ (n - 1)] and A equals {[}m/ (n -1 )]. Below this threshold, T equals delta, and we give a two-value concentration result for the arboricity A in that range. Finally, we include a stronger version of these results in the context of the random graph process where the edges are randomly added one by one. A direct application of our result gives a sharp threshold for the maximum load being at most k in the two-choice load balancing problem, where k -> infinity. (AU) | |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |