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- W2609209176 abstract "A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. The study of rainbow decompositions has a long history, going back to the work of Euler on Latin squares. In this paper we discuss three problems about decomposing complete graphs into rainbow trees: the Brualdi–Hollingsworth Conjecture, Constantine's Conjecture, and the Kaneko–Kano–Suzuki Conjecture. We show that in every proper edge-colouring of Kn there are 10−6n edge-disjoint spanning isomorphic rainbow trees. This simultaneously improves the best known bounds on all these conjectures. Using our method we also show that every properly (n−1)-edge-coloured Kn has n/9−6 edge-disjoint rainbow trees, giving further improvement on the Brualdi–Hollingsworth Conjecture." @default.
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- W2609209176 date "2018-09-01" @default.
- W2609209176 modified "2023-09-24" @default.
- W2609209176 title "Linearly many rainbow trees in properly edge-coloured complete graphs" @default.
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- W2609209176 doi "https://doi.org/10.1016/j.jctb.2018.03.005" @default.
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