Decomposing Complete Equipartite Multigraphs into Cycles of Variable Lengths: The Amalgamation-detachment Approach

作者：Bahmanian M Amin^*; Sajna Mateja^*

来源：Journal of Combinatorial Designs, 2016, 24(4): 165-183.

DOI：10.1002/jcd.21419

• complete equipartite multigraph
• Alspach's conjecture
• cycle decomposition
• amalgamation
• detachment

Using the technique of amalgamation-detachment, we show that the complete equipartite multigraph can be decomposed into cycles of lengths (plus a 1-factor if the degree is odd) whenever there exists a decomposition of into cycles of lengths (plus a 1-factor if the degree is odd). In addition, we give sufficient conditions for the existence of some other, related cycle decompositions of the complete equipartite multigraph lambda K-nxm.

• 出版日期2016-4