Skip to main content Accessibility help
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 7 - Supersaturated graphs in the edge-triangle model

  • Charles Radin, University of Texas at Austin, Lorenzo Sadun, University of Texas at Austin
  • Book:
    Emergence and Phase Transitions in Uniform Random Graphs
    Print publication:
    26 November 2026, pp 126-157

  • Summary

    The main result of this chapter is a proof of the existence of a bipodal phase just above the entire length of the curve bisecting the Razborov triangle. This requires separate arguments for e < ½, e > ½, and e approximately ½, with the arguments governing overlapping regions whose union stretches all the way from e = 0 to e = 1. We previously proved the existence of a bipodal phase just below the top boundary of the Razborov triangle in Chapter 4. It is likely, but as yet unproven, that these two regions are part of a single F(1,1) phase covering the entire region where $t>e^3$. We then show that these results are not specific to the edge-triangle model. In every "edge-H" model where we constrain the densities of edges and one other graph H, we prove that there is an F(1,1)-like bipodal phase lying above all but finitely points of the Erdős–Rényi curve.