On the non-3-colourability of random graphs

Abstract

We 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 figure

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• Typical random 3-SAT formulae and the satisfiability threshold