Arboricity and spanning-tree packing in random graphs

Autor(es)

Gao, Pu ^[1] ; Perez-Gimenez, Xavier ^[2] ; Sato, Cristiane M. ^[3]

Afiliação do(s) autor(es)

^[1] Monash Univ, Melbourne, Vic - Australia

^[2] Univ Nebraska, Lincoln, NE - USA

^[3] Univ Fed ABC, Ctr Math Comp & Cognit, Santo Andre - Brazil

• Tipo de documento: Artigo Científico
• Fonte: RANDOM STRUCTURES & ALGORITHMS; v. 52, n. 3, p. 495-535, MAY 2018.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 13/03447-6 - Estruturas combinatórias, otimização e algoritmos em Teoria da Computação
• Beneficiário: Carlos Eduardo Ferreira
• Modalidade de apoio: Auxílio à Pesquisa - Temático