On random irregular subgraphs

Abstract

Let be a ‐regular graph on vertices. Frieze, Gould, Karoński, and Pfender began the study of the following random spanning subgraph model . Assign independently to each vertex of a uniform random number , and an edge of is an edge of if and only if . Addressing a problem of Alon and Wei, we prove that if , then with high probability, for each nonnegative integer , there are vertices of degree in .