Solitary subgraphs of random graphs (Q1970715)

This paper generalizes a result of \textit{W. C. S. Suen} that appeared in [Random Struct. Algorithms 1, No.~2, 231-242 (1990; Zbl 0747.05082)]. Fix a graph \(H\) and consider the number \(Z(H)\) of copies of \(H\) in a random graph, \(G(n,p)\), that are vertex disjoint. This paper identifies the threshold for when \(Z(H)\) becomes zero in the case when \(G(n,p)\) is strictly balanced. The paper by Suen considers a more restricted class of graphs. Results for the class of balanced graphs are also presented but the meat of the result is in the strictly balanced case.