Resolution of the Oberwolfach problem

DOI10.4171/JEMS/1060zbMath1473.05241arXiv1806.04644OpenAlexW2980371990MaRDI QIDQ2039583

Deryk Osthus, Stefan Glock, Jae-Hoon Kim, Felix Joos, Daniela Kühn

Publication date: 5 July 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04644

zbMATH Keywords

cyclesdecompositionsresolvable designs2-factors

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Paths and cycles (05C38) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Combinatorial aspects of packing and covering (05B40) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40) Graph designs and isomorphic decomposition (05C51)

Related Items

On the Oberwolfach problem for single-flip 2-factors via graceful labelings ⋮ Decompositions of quasirandom hypergraphs into hypergraphs of bounded degree ⋮ A greedy algorithm for the social golfer and the Oberwolfach problem ⋮ A Short proof of the blow-up lemma for approximate decompositions ⋮ On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform‐length cycles ⋮ Graph and hypergraph colouring via nibble methods: a survey ⋮ A complete solution to the infinite Oberwolfach problem ⋮ Graph and hypergraph packing ⋮ A constructive solution to the Oberwolfach problem with a large cycle ⋮ A rainbow blow-up lemma for almost optimally bounded edge-colourings ⋮ On the generalized Oberwolfach problem ⋮ On zero-sum spanning trees and zero-sum connectivity ⋮ Decomposing hypergraphs into cycle factors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A complete solution to the two-table Oberwolfach problems
• Asymptotic behavior of the chromatic index for hypergraphs
• Complete solutions to the Oberwolfach problem for an infinite set of orders
• On a variation of the Oberwolfach problem
• The existence of \(C_ k\)-factorizations of \(K_{2n}-F\)
• The solution of the bipartite analogue of the Oberwolfach problem
• On the Hamilton-Waterloo problem
• Blow-up lemma
• Counting designs
• The Oberwolfach problem and factors of uniform odd length cycles
• Hamilton decompositions of regular expanders: A proof of Kelly's conjecture for large tournaments
• Optimal packings of bounded degree trees
• Packing degenerate graphs
• On the decomposition threshold of a given graph
• On a hypergraph matching problem
• Packing spanning graphs from separable families
• SOME RESULTS ON THE OBERWOLFACH PROBLEM
• On bipartite 2-factorizations of kn − I and the Oberwolfach problem
• Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture
• Fractional Triangle Decompositions in Graphs with Large Minimum Degree
• A blow-up lemma for approximate decompositions
• A Fast Approximation Algorithm for Computing the Frequencies of Subgraphs in a Given Graph
• A bandwidth theorem for approximate decompositions
• Cycle decompositions V: Complete graphs into cycles of arbitrary lengths
• Merging Combinatorial Design and Optimization: the Oberwolfach Problem
• Proof of the 1-factorization and Hamilton Decomposition Conjectures
• Fractional Clique Decompositions of Dense Partite Graphs
• The Existence of Designs via Iterative Absorption: Hypergraph 𝐹-designs for Arbitrary 𝐹
• Edge-decompositions of graphs with high minimum degree