Erratum to: “Star factorizations of graph products”

This erratum concerns the two theorems in Section 4 of the article “Star Factorizations of Graph Products” by Bryant, El-Zanati, and Vanden Eynden [1]. The statement of Theorem 5 is false and is thus being withdrawn. The statement of Theorem 6 holds; however, the proof given in the original manuscript uses Theorem 5. Here, we offer a proof of Theorem 6. The rest of the article is not affected by these changes. For a positive integer j, the graph K1,j, is the graph of the j-star and is denoted by Sj. Let k be a positive integer and r1, r2, . . . , rk integers greater than 2. Let ∏k i=1 Cri denote the Cartesian product of the cycles Cr1, Cr2, . . . , Crk . In Theorem 5, it is claimed that there exists an Sk-factorization of ∏k i=1 Cri if and only if k + 1| ∏ki=1 ri. This statement is false. In fact, we can now prove (through Journal of Graph Theory © 2006 Wiley Periodicals, Inc.