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

DOI10.1002/jcd.21419zbMath1338.05208arXiv1909.09644OpenAlexW3125459157MaRDI QIDQ2804929

Mateja Šajna, M. Amin Bahmanian

Publication date: 6 May 2016

Published in: Journal of Combinatorial Designs (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.09644

zbMATH Keywords

detachmentamalgamationcycle decompositionAlspach's conjecturecomplete equipartite multigraph

Mathematics Subject Classification ID

Paths and cycles (05C38) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (10)

Decomposing \(K_{u + w} - K_u\) into cycles of prescribed lengths ⋮ Decomposition of a complete bipartite multigraph into arbitrary cycle sizes ⋮ Resolvable cycle decompositions of complete multigraphs and complete equipartite multigraphs via layering and detachment ⋮ Cyclic cycle systems of the complete multipartite graph ⋮ Decomposition of the tensor product of complete graphs into cycles of lengths 3 and 6 ⋮ Decompositions of some classes of dense graphs into cycles of lengths 4 and 8 ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Decomposition of complete equipartite graphs into paths and cycles of length \(2p\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hamiltonian decompositions of complete graphs
• Path and cycle decompositions of complete equipartite graphs: 3 and 5 parts
• Path and cycle decompositions of complete equipartite graphs: Four parts
• Hamiltonian decompositions of complete regular s-partite graphs
• Decomposition of K//(m,n)(K*//(m,n)) into cycles (circuits) of length 2k
• On decomposition of r-partite graphs into edge-disjoint Hamilton circuits
• Balanced incomplete block designs and related designs
• Decomposition of \(K_{m,n}\) into short cycles
• Cycle systems in the complete bipartite graph minus a one-factor
• Decomposing various graphs into short even-length cycles
• Decomposing complete equipartite graphs into short odd cycles
• Decompositions of complete multipartite graphs into cycles of even length
• \(C_{p}\)-decompositions of some regular graphs
• Decomposition of \(K_{m, n}\) into 4-cycles and \(2t\)-cycles
• Decomposing complete equipartite graphs into odd square-length cycles: number of parts odd
• Decomposing complete equipartite graphs into short even cycles
• Decomposing complete equipartite graphs into cycles of length2p
• Cycle decompositions V: Complete graphs into cycles of arbitrary lengths
• Cycle Decompositions of $K_{\lowercase{n,n}}-I$
• Cycle decompositions of complete multigraphs

This page was built for publication: Decomposing Complete Equipartite Multigraphs into Cycles of Variable Lengths: The Amalgamation-detachment Approach