Kotzig's cyclic tree decomposition conjecture

About 10 years old · traced to

Let TT be a tree with n+1n+1 vertices, and identify the vertices of K2n+1K_{2n+1} with the integers modulo 2n+12n+1. A cyclic decomposition into copies of TT consists of the cyclic shifts of one copy of TT forming an edge decomposition. Ringel--Kotzig conjecture. For any (n+1)(n+1)-vertex tree TT, the complete graph K2n+1K_{2n+1} can be cyclically decomposed into copies of TT. 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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.