The Directed Anti-Oberwolfach Solution: Pancyclic 2-Factorizations of Complete Directed Graphs of Odd Order

Brett Stevens

Abstract


The directed anti-Oberwolfach problem asks for a 2-factorization (each factor has in-degree 1 and out-degree 1 for a total degree of two) of $K_{2n+1}$, not with consistent cycle components in each 2-factor like the Oberwolfach problem, but such that every admissible cycle size appears at least once in some 2-factor. The solution takes advantage of both Piotrowski's decomposition techniques used to solve Oberwolfach problems and the techniques used by the author to solve the undirected anti-Oberwolfach problem.


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