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DECOMPOSING COMPLETE GRAPHS INTO CUBES
| Content Provider | CiteSeerX |
|---|---|
| Author | Eynden, En El-Zanati, Saad I. |
| Abstract | This paper concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n be congruent to 1 modulo d and 0 modulo 2d. These are known to be sufficient for d equal to 3 or 5. For larger values of d, the necessary conditions are asymptotically sufficient by Wilson’s results. We prove that for each odd d there is an infinite arithmetic progression of even integers n for which a decomposition exists. This lends further weight to a long-standing conjecture of Kotzig. |
| File Format | |
| Access Restriction | Open |
| Content Type | Text |
