The blue-edge density conjecture for the diamond-free process

Let GMG_M be the final graph produced by the diamond-free process, and let GblueG_{blue} denote its subgraph of blue edges. Write e(G)e(G) for the number of edges of a graph GG.

Blue-edge density conjecture. As nn\to\infty,

e(Gblue)=(23+o(1))e(GM).e(G_{blue}) = \left( \frac{2}{3} + o(1) \right)e(G_M).

The theorem preceding this conjecture establishes the analogous estimate at the intermediate time mm, with high probability. The authors expect the same asymptotic proportion to persist in the final graph, but the statement is presented as an unproved conjecture.

Sources & referencesView supporting material

Primary source

Michael E. Picollelli, “The diamond-free process”, arXiv:1010.5207 (2010).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.