標題: (4,5)-CYCLE SYSTEMS OF COMPLETE MULTIPARTITE GRAPHS
作者: Huang, Ming-Hway
Fu, Hung-Lin
應用數學系
Department of Applied Mathematics
關鍵字: Cycle system;Alspach conjecture;Cycle decomposition
公開日期: 1-Jun-2012
摘要: In 1981, Alspach conjectured that if 3 <= m(i) <= v, v is odd and v(v - 1)/2 = m(1) +m(2)+ ... +m(t) then the complete graph K-v can be decomposed into t cycles of lengths m(1), m(2), ... , m(t) respectively; if v is even, v(v - 2)/2 = m(1) + m(2) ... + m(t), then the complete graph minus a one-factor K-v - F can be decomposed into t cycles of lengths m(1), m(2),..., Tat respectively. In this paper, we extend the study to the decomposition of the complete equipartite graph K-m(n).For m(i) is an element of {4, 5}, we prove that the trivial necessary conditions are also sufficient.
URI: http://dx.doi.org/10.11650/twjm/1500406672
http://hdl.handle.net/11536/150480
ISSN: 1027-5487
DOI: 10.11650/twjm/1500406672
期刊: TAIWANESE JOURNAL OF MATHEMATICS
Volume: 16
起始頁: 999
結束頁: 1006
Appears in Collections:Articles