Adding random edges to dense graphs

Authors:
Tom Bohman;Alan Frieze;Michael Krivelevich;Ryan Martin
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania;Department of Mathematics, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania
Venue:
Random Structures & Algorithms
Year:
2004

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Abstract

This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small diameter and k-connectivity.