Primitive cycle decompositions of Kn and Kn−I

DOI10.1002/jcd.21817zbMath1529.05090OpenAlexW4206363353MaRDI QIDQ6146186

Michael William Schroeder, Unnamed Author, John Asplund, Chandra Dinavahi

Publication date: 5 February 2024

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

Full work available at URL: https://doi.org/10.1002/jcd.21817

zbMATH Keywords

subsystemscycle decompositioncycle systemsubdecompositionprimitive (cycle) decomposition

Mathematics Subject Classification ID

Paths and cycles (05C38) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Graph designs and isomorphic decomposition (05C51)

Cites Work

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• Hamiltonian decomposition of Cayley graphs of degree 4
• Decomposition of K//(m,n)(K*//(m,n)) into cycles (circuits) of length 2k
• On decomposing \(K_n -I\) into cycles of a fixed odd length
• Skolem-type difference sets for cycle systems
• Cycle decompositions of \(K_n\) and \(K_n-I\)
• Existence of cyclic \(k\)-cycle systems of the complete graph
• Existence of 1-rotational \(k\)-cycle systems of the complete graph
• Sur la structure de certains systèmes triples de Steiner
• Cycle decompositions III: Complete graphs and fixed length cycles
• Cyclic even cycle systems of the complete graph
• On the construction of odd cycle systems
• Rotational k‐cycle systems of order v < 3k; another proof of the existence of odd cycle systems

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