It was shown false by Thomason (1989) for all t4. We present a class of simply describable Cayley graphs which also show the falsity of Erds conjecture for t = 4. These graphs were found by a computer search and, although of large orders (2¹⁰-2¹⁴), they are rather simple and highly regular. The smallest upper bound for c₄ obtained by us is 0.976501 x , and is given by the graph on the power set of a 10-element set (and, hence, of order 2¹⁰) determined by the configuration {1,3,4,7,8,10}. and by the graph on the power set of 11 elements (and, hence, of order 2¹¹) determined by the configuration {1,3,4,7,8,10,11}. It is also shown that the ratio of edges to nonedges in a sequence contradicting the conjecture for t = 4 may approach 1, unlike in the sequences of graphs Thomason used in 1989.