2 problems

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The spouse-loving Oberwolfach conjecture for four groups of odd cycle length
Let $m$ be a positive odd integer. The spouse-loving variant of the Oberwolfach problem, denoted $\operatorname{OP}^+(n;m)$ , asks whether the graph $K_n+I$ admits a $C_m$ -factoriza…
Conjectureopencycle-factorizations graph-decompositions oberwolfach-problemarXiv posted 2 days ago
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Burgess–Sajna conjecture on directed cycle factorizations of complete symmetric digraphs
Burgess–Sajna conjecture. The digraph $K_{2m}^{*}$ admits a directed $m$ -cycle factorization if and only if
Conjectureopencycle-factorizations directed-graphs graph-decompositionsarXiv posted 2 days ago

The spouse-loving Oberwolfach conjecture for four groups of odd cycle length