Hell, PavolMiller, D.J.2009-08-202009-08-2019882009-08-20http://hdl.handle.net/1828/1555In this paper we investigate the achromatic number of the disjoint union of graphs and the achromatic number of the categorical product of graphs. We obtain the best possible upper and lower bounds for the union of graphs and the best possible lower bound for the product of graphs. Finally we show that the achromatic number of the product of graphs is bounded above.entechnical reports (mathematics and statistics)Technical ReportDepartment of Mathematics and Statistics