Adding random edges to dense graphs
Tom Bohman, Alan Frieze, Michael Krivelevich, Ryan R. Martin
TL;DR
This paper explores how adding random edges to dense graphs can induce properties like cliques, small diameter, and connectivity, providing thresholds for these features to emerge.
Contribution
It determines the minimum number of random edges needed to guarantee various monotone properties in dense graphs.
Findings
Thresholds for clique appearance
Conditions for small diameter
Criteria for k-connectivity
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 -connectivity.
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