The Hamilton-Waterloo problem for cycle sizes 3 and 4

DOI10.1002/jcd.20219zbMath1222.05119OpenAlexW2043898581MaRDI QIDQ3578158

Peter Danziger, Brett Stevens, Gaetano Quattrocchi

Publication date: 13 July 2010

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

Full work available at URL: https://doi.org/10.1002/jcd.20219

zbMATH Keywords

cycle decompositionsgraph factorizationsHamilton-Waterloo problemresolvable graph decompositionsuniform resolutions

Mathematics Subject Classification ID

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

Related Items (20)

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 ⋮ On bipartite 2-factorizations of kn − I and the Oberwolfach problem ⋮ The Hamilton-Waterloo problem with 4-cycles and a single factor of \(n\)-cycles ⋮ A note on the Hamilton-Waterloo problem with \(C_8\)-factors and \(C_m\)-factors ⋮ Hamilton cycle rich 2-factorization of complete equipartite graphs. II ⋮ On the existence of uniformly resolvable decompositions of \(K_v\) and \(K_v-I\) into paths and kites ⋮ Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem ⋮ Uniformly resolvable cycle decompositions with four different factors ⋮ 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 ⋮ On the Hamilton‐Waterloo Problem for Bipartite 2‐Factors ⋮ Unnamed Item ⋮ The Hamilton-Waterloo problem for triangle-factors and heptagon-factors ⋮ The Hamilton-Waterloo problem: The case of triangle-factors and one Hamilton cycle ⋮ On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity ⋮ The Hamilton-Waterloo problem with even cycle lengths ⋮ Unnamed Item

Cites Work

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• Maximum uniformly resolvable designs with block sizes 2 and 4
• Frames for Kirkman triple systems
• Uniformly resolvable pairwise balanced designs with blocksizes two and three
• Class-uniformly resolvable pairwise balanced designs with block size two and three
• On the Hamilton-Waterloo problem
• On the Oberwolfach problem for complete multigraphs
• Class-uniformly resolvable group divisible structures. I: Resolvable group divisible designs
• Class-uniformly resolvable group divisible structures. II: Frames
• Geometrical constructions of class-uniformly resolvable structure
• Two new infinite families of extremal class-uniformly resolvable designs

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