Erdős's monochromatic triangle packing conjecture

From papers

Let KnK_n be the complete graph on nn vertices whose edges are coloured with two colours. A collection of triangles is pairwise edge-disjoint if no edge belongs to more than one triangle. Erdős's conjecture. Every 22-coloured KnK_n contains n2/12+o(n2)n^2/12 + o(n^2) pairwise edge-disjoint monochromatic triangles. This conjecture asks for the asymptotically sharp guaranteed size of a monochromatic triangle packing in every two-edge-colouring of a complete graph; the paper's abstract says that it confirms the conjecture.

Progress summary

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

Sources & referencesView supporting material

Primary source

Vytautas Gruslys and Shoham Letzter, “Monochromatic triangle packings in red-blue graphs”, arXiv:2008.05311 (2020).

Additional references

2 papers in this index state this conjecture (2020). The statement above is taken from the most recent of them; the others are arXiv:2001.00763.

Solutions 0

No solutions have been posted yet.