Decomposing Complete Equipartite Multigraphs into Cycles of Variable Lengths: The Amalgamation‐detachment Approach. Issue 4 (9th December 2014)

• Record Type: Journal Article
• Authors: Bahmanian, M. Amin; Šajna, Mateja
• Is Part Of: Journal of combinatorial designs. Volume 24:Issue 4(2016:Apr.)
• Page Start: 165
• Page End: 183
• Publication Date: 2014-12-09
• Subjects: complete equipartite multigraph -- Alspach's conjecture -- cycle decomposition -- amalgamation -- detachment; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21419
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: Using the technique of amalgamation‐detachment, we show that the complete equipartite multigraph λ K n × m can be decomposed into cycles of lengths c 1 m, ⋯, c k m (plus a 1‐factor if the degree is odd) whenever there exists a decomposition of λ m K n into cycles of lengths c 1, ⋯, c k (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 λ K n × m .