Spanning trees at the connectivity threshold
Yahav Alon, Michael Krivelevich, Peleg Michaeli
TL;DR
This paper constructs an explicit spanning structure that emerges in a random graph immediately after it becomes connected, providing insights into the connectivity threshold behavior.
Contribution
It introduces a specific connected spanning structure that appears at the connectivity threshold in random graphs, enhancing understanding of phase transitions.
Findings
Structure appears with high probability just above the threshold
Provides explicit construction of the spanning structure
Advances understanding of connectivity phase transition
Abstract
We present an explicit connected spanning structure that appears in a random graph just above the connectivity threshold with high probability.
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Taxonomy
TopicsInterconnection Networks and Systems · Complex Network Analysis Techniques · Stochastic processes and statistical mechanics