ON THE PRODUCT OF THE POINT AND LINE COVERING NUMBERS OF A GRAPH

where G ranges over all graphs with n points . He further noted that equality holds in 61 forthe star K,,,_, and in (ii) for the complete graph K,, . In this note we settle these conjectures . In particular, we show that (i) is true, and ,ii), while not completely true, is nearly true . The smallest countterexampl . to (ii) is the graph 2K3 consisting of two disjoint triangles . Note that a0(2K3),xt(2K3) = 16, ao(K6)o:,(K6) = 15 . imvover (1!) k valid it n ±3 odd o .' : G is reclinred to be connected! . "Vc nlst : consider' the corresponding questions for hypergraplis .