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A graph G is called (K 3, K3)-co-critical if the edges of G can be coloured with two colours without getting a monochromatic triangle, but adding any new edge to the graph, this kind of 'good' colouring is impossible. In this short note we construct (K 3, K3)-co-critical graphs of maximal degree O(n3/4). * Corresponding address. 0012-365X/96/$15.00 ~(2' 1996 Elsevier Science B.V. All rights reserved SSDI 0012-365X(95)00121-2doi:10.1016/0012-365x(95)00121-c fatcat:rhthb4zvtjgz7ocxkyaolujq7a