TY - JOUR

T1 - An asymptotic solution to the cycle decomposition problem for complete graphs

AU - Bryant, Darryn

AU - Horsley, Daniel

PY - 2010

Y1 - 2010

N2 - Let m1,m2, . . . ,mt be a list of integers. It is shown that there exists an
integer N such that for all n N, the complete graph of order n can be
decomposed into edge-disjoint cycles of lengths m1,m2, . . . ,mt if and only if n is odd, 3 mi n for i = 1, 2, . . . , t, and m1 + m2 + A? A? A?mt =
2 taken from n elements. In 1981, Alspach conjectured that this result holds for all n, and that a corresponding
result also holds for decompositions of complete graphs of even order into cycles and a perfect matching

AB - Let m1,m2, . . . ,mt be a list of integers. It is shown that there exists an
integer N such that for all n N, the complete graph of order n can be
decomposed into edge-disjoint cycles of lengths m1,m2, . . . ,mt if and only if n is odd, 3 mi n for i = 1, 2, . . . , t, and m1 + m2 + A? A? A?mt =
2 taken from n elements. In 1981, Alspach conjectured that this result holds for all n, and that a corresponding
result also holds for decompositions of complete graphs of even order into cycles and a perfect matching

UR - http://www.aarms.math.ca/paper/an-asymptotic-solution-to-the-cycle-decomposition-.pdf

U2 - 10.1016/j.jcta.2010.03.015

DO - 10.1016/j.jcta.2010.03.015

M3 - Article

VL - 117

SP - 1258

EP - 1284

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 8

ER -