2023
DOI: 10.1002/rsa.21197
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Sharp thresholds in adaptive random graph processes

Calum MacRury,
Erlang Surya

Abstract: The ‐process is a single player game in which the player is initially presented the empty graph on vertices. In each step, a subset of edges is independently sampled according to a distribution . The player then selects one edge from , and adds to its current graph. For a fixed monotone increasing graph property , the objective of the player is to force the graph to satisfy in as few steps as possible. The ‐process generalizes both the Achlioptas process and the semi‐random graph process. We prove a suffi… Show more

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