A proof of Ringel’s conjecture

A typical decomposition question asks whether the edges of some graph G can be partitioned into disjoint copies of another graph H . One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree....

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Published inGeometric and functional analysis Vol. 31; no. 3; pp. 663 - 720
Main Authors Montgomery, R., Pokrovskiy, A., Sudakov, B.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2021
Springer Nature B.V
Subjects
Analysis
Decomposition
Graph theory
Mathematics
Mathematics and Statistics
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Summary:A typical decomposition question asks whether the edges of some graph G can be partitioned into disjoint copies of another graph H . One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with n edges packs 2 n + 1 times into the complete graph K 2 n + 1 . In this paper, we prove this conjecture for large n .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-021-00576-2