Kotzig's cyclic tree decomposition conjecture
Let be a tree with vertices, and identify the vertices of with the integers modulo . A cyclic decomposition into copies of consists of the cyclic shifts of one copy of forming an edge decomposition. Ringel--Kotzig conjecture. For any -vertex tree , the complete graph can be cyclically decomposed into copies of . This strengthens Ringel's conjecture by requiring the decomposition to arise from cyclic shifts, and remains open in the source's discussion.
References
Primary source
Anna Adamaszek, Peter Allen, Codrut Grosu and Jan Hladky, “Almost all trees are almost graceful”, arXiv:1608.01577 (2019).
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