Ryser's conjecture on rainbow cycle packings
Let be the complete directed graph with both directed edges between every pair of vertices and a loop at every vertex, properly edge-coloured with colours. A rainbow spanning subgraph is one whose edges have distinct colours.
Ryser's conjecture. If is odd, then contains a rainbow spanning subgraph in which every vertex has in-degree and out-degree equal to one. Equivalently, can be packed with directed cycles in a rainbow fashion.
This is a conjecture about rainbow cycle decompositions of properly coloured complete directed graphs. The paper presents it as a famous open problem and discusses related strengthening by prescribing cycle lengths.
References
Primary source
Alp Müyesser, “Cycle type in Hall-Paige: A proof of the Friedlander-Gordon-Tannenbaum conjecture”, arXiv:2303.16157 (2023).
Progress summary
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.