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Decompositions into isomorphic rainbow spanning trees

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 نشر من قبل Richard Montgomery
 تاريخ النشر 2019
  مجال البحث
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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.



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