TY - JOUR

T1 - A note on cyclic m-cycle systems of K r(m)

AU - Wu, Shung Liang

AU - Fu, Hung-Lin

PY - 2006/11/1

Y1 - 2006/11/1

N2 - 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) ≠ (3, 3) and (c) (r,m) ≢ (t , 2) (mod 4) where t ∈ {2,3}.

AB - 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) ≠ (3, 3) and (c) (r,m) ≢ (t , 2) (mod 4) where t ∈ {2,3}.

UR - http://www.scopus.com/inward/record.url?scp=33751526008&partnerID=8YFLogxK

U2 - 10.1007/s00373-006-0658-z

DO - 10.1007/s00373-006-0658-z

M3 - Article

AN - SCOPUS:33751526008

VL - 22

SP - 427

EP - 432

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 3

ER -