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Factorizations of complete multipartite graphs into generalized cubes

✍ Scribed by El--Zanati, S.; Vanden Eynden, C.

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 100 KB
Volume: 33
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(200003)33:3<144::aid-jgt4>3.0.co;2-p

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✦ Synopsis

For a positive integer d, the usual d-dimensional cube Q d is defined to be the graph (K 2 ) d , the Cartesian product of d copies of K 2 . We define the generalized cube Q(K k , d) to be the graph (K k ) d for positive integers d and k. We investigate the decomposition of the complete multipartite graph K k j ×k n-j into factors that are vertex-disjoint unions of generalized cubes Q(K k , d i ), where k is a power of a prime, n and j are positive integers with j ≤ n, and the d i may be different in different factors. We also use these results to partially settle a problem of Kotzig on Q d -factorizations of K n .

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