2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64883We show that for c >= 2.4682, a random graph on n vertices with c n (1+o(1)) edges almost surely has no 3-colouring. This improves on the current best upper bound of 2.4947.9 pages, 1 figureCombinatorics05C80; 05C15text