Octahedral, dicyclic and special linear solutions of some Hamilton-Waterloo problems

DOI10.26493/1855-3974.1088.414zbMath1391.05201OpenAlexW2963990843WikidataQ129389277 ScholiaQ129389277MaRDI QIDQ3174791

Marco Buratti, Simona Bonvicini

Publication date: 18 July 2018

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.26493/1855-3974.1088.414

zbMATH Keywords

group actionspecial linear groupHamilton-Waterloo problemdicyclic groupoctahedral binary group

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Group actions on combinatorial structures (05E18)

Related Items (15)

Uniformly resolvable decompositions of \(K_v\) into \(K_2\) and \(K_{1, 3}\) graphs ⋮ A cyclic solution for an infinite class of Hamilton-Waterloo problems ⋮ Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles ⋮ Octahedral, dicyclic and special linear solutions of some Hamilton-Waterloo problems ⋮ A note on the Hamilton-Waterloo problem with \(C_8\)-factors and \(C_m\)-factors ⋮ Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem ⋮ Completing the spectrum of almost resolvable cycle systems with odd cycle length ⋮ The Hamilton-Waterloo problem with \(C_4\) and \(C_m\) factors ⋮ Further results on almost resolvable cycle systems and the Hamilton–Waterloo problem ⋮ On the Hamilton-Waterloo problem with cycle lengths of distinct parities ⋮ Unnamed Item ⋮ Uniformly resolvable decompositions of \(K_v\) into paths on two, three and four vertices ⋮ On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity ⋮ The Hamilton-Waterloo problem with even cycle lengths ⋮ Factorizations of complete graphs into cycles and 1-factors

Cites Work

• A complete solution to the two-table Oberwolfach problems
• The Hamilton-Waterloo problem with \(C_4\) and \(C_m\) factors
• Some progress on the existence of 1-rotational Steiner triple systems
• Complete solutions to the Oberwolfach problem for an infinite set of orders
• 1-Rotational Steiner triple systems over arbitrary groups
• Octahedral, dicyclic and special linear solutions of some Hamilton-Waterloo problems
• Rotational k‐cycle systems of order v < 3k; another proof of the existence of odd cycle systems
• Unnamed Item

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