標題: | A note on cyclic m-cycle systems of K-r((m)) |
作者: | Wu, Shung-Liang Fu, Hung-Lin 應用數學系 Department of Applied Mathematics |
公開日期: | 1-Nov-2006 |
摘要: | It was proved by Buratti and Del Fra that for each pair of odd integers r and m, there exists a cyclic m-cycle system of the balanced complete r-partite graph K-r(m) except for the case when r=m=3. In this note, we study the existence of a cyclic m-cycle system of K-r(m) where r or m is even. Combining the work of Buratti and Del Fra, we prove that cyclic m-cycle systems of K-r(m) exist if and only if (a) K-r(m) is an even graph (b) (r, m) not equal (3, 3) and (c) (r,m) not equivalent to (t , 2) (mod 4) where t is an element of {2,3}. |
URI: | http://dx.doi.org/10.1007/s00373-006-0658-z http://hdl.handle.net/11536/11643 |
ISSN: | 0911-0119 |
DOI: | 10.1007/s00373-006-0658-z |
期刊: | GRAPHS AND COMBINATORICS |
Volume: | 22 |
Issue: | 3 |
起始頁: | 427 |
結束頁: | 432 |
Appears in Collections: | Articles |
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