Decompositions into isomorphic rainbow spanning trees

Stefan Glock; Daniela Kuhn; Richard Montgomery; Deryk Osthus

doi:10.1016/j.jctb.2020.03.002

Decompositions into isomorphic rainbow spanning trees

Stefan Glock, Daniela Kuhn, Richard Montgomery, Deryk Osthus

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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Abstract

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. Our main result implies that, given any optimal colouring of a sufficiently large complete graph K_2n, there exists a decomposition of K_2n into isomorphic rainbow spanning trees. This settles conjectures of Brualdi-Hollingsworth (from 1996) and Constantine (from 2002) for large graphs.

Original language	English
Pages (from-to)	439-484
Journal	Journal of Combinatorial Theory. Series B
Volume	146
DOIs	https://doi.org/10.1016/j.jctb.2020.03.002
Publication status	Published - 10 Mar 2020

Keywords

Absorption
Hypergraph matchings
Rainbow decompositions
Rainbow spanning trees

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2020.03.002Licence: None: All rights reserved

Glock_et_al_Decompositions_into_isomorphic_rainbow_spanning_trees_JCTB_2020Accepted author manuscript, 620 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

https://www.sciencedirect.com/science/article/pii/S0095895620300113Licence: None: All rights reserved

Cite this

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title = "Decompositions into isomorphic rainbow spanning trees",

abstract = "A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. Our main result implies that, given any optimal colouring of a sufficiently large complete graph K2n, there exists a decomposition of K2n into isomorphic rainbow spanning trees. This settles conjectures of Brualdi-Hollingsworth (from 1996) and Constantine (from 2002) for large graphs.",

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AU - Osthus, Deryk

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AB - A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. Our main result implies that, given any optimal colouring of a sufficiently large complete graph K2n, there exists a decomposition of K2n into isomorphic rainbow spanning trees. This settles conjectures of Brualdi-Hollingsworth (from 1996) and Constantine (from 2002) for large graphs.

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Decompositions into isomorphic rainbow spanning trees

Abstract

Keywords

ASJC Scopus subject areas

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