Achromatic numbers and graph operations
Many papers have been written on colourings and chromatic numbers, but not so many ones on achromatic numbers. While the chromatic number of a given graph \(X\) is the smallest \(n\) for which \(X\) admits a complete \(n\)- colouring, the achromatic number is the largest one with the same property. The authors study this branch of graph theory. They investigate the achromatic number of the disjoint union of graphs and the best possible lower bound for the categorical product of graphs. On the other hand, they show a surprising example of two graphs both with achromatic number exactly \(a\) such that their product has achromatic number approximately equal to \((a)^{a^ 2/2}\). Finally the authors show that the achromatic number of the product of graphs is bounded above.
scientific article; zbMATH DE number 97510
scientific article