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Barak, A.B. and Erdös, P. (1984) On the Maximal Number of Strongly Independent Vertices in a Random Acyclic Directed Graph. SIAM Journal on Algebraic Discrete Methods, 5, 508-514.

has been cited by the following article:

• TITLE: Improved Approximation of Layout Problems on Random Graphs

  AUTHORS: Kevin K. H. Cheung, Patrick Girardet

  KEYWORDS: Graph Arrangements, Random Graphs, Approximation Algorithms, Undirected Graphs, Directed Acyclic Graphs

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.10 No.1, January 10, 2020

  ABSTRACT: Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs, Discrete Mathematics, 235, 2001, 245-253), we show that several well-known graph layout problems are approximable to within a factor arbitrarily close to 1 of the optimal with high probability for random graphs drawn from an Erdös-Renyi distribution with appropriate sparsity conditions using only elementary probabilistic analysis. Moreover, we show that the same results hold for the analogous problems on directed acyclic graphs.