Suppose that S1,...,SN are collections of subsets of X1,...,XN, respectively, such that ni subsets belonging to Si, and no fewer, cover Xi for all i. the main result of this paper is that to cover X1 x...x XN requires no fewer than σNi=1 (ni-1) + 1 and no more than ΠNi=1ni subsets of the form A1 x...x AN, where Ai∈S1 for all i. Moreo ver, these bounds cannot be improved. Identical bounds for the spanning number of a normal product of graphs are also obtained.
Bibliographical noteFunding Information:
* This paper presents the results of one phase of research carria,d oui at :he Jet Propulsion Laboratory, California Institute of Technology, under Contrxt No. NAS 7-100, sponsored by the National Aeronautics a1.d Space Administration. ** Original version received 15 November 1971.