- Publication venue
- Publication date
- 21/09/2023
- Field of study
The directed Oberwolfach problem OPβ(m1β,β¦,mkβ) asks whether the
complete symmetric digraph Knββ, assuming n=m1β+β¦+mkβ, admits a
decomposition into spanning subdigraphs, each a disjoint union of k directed
cycles of lengths m1β,β¦,mkβ. We hereby describe a method for
constructing a solution to OPβ(m1β,β¦,mkβ) given a solution to
OPβ(m1β,β¦,mββ), for some β<k, if certain conditions on
m1β,β¦,mkβ are satisfied. This approach enables us to extend a solution
for OPβ(m1β,β¦,mββ) into a solution for
OPβ(m1β,β¦,mββ,t), as well as into a solution for
OPβ(m1β,β¦,mββ,2β¨tβ©), where 2β¨tβ© denotes t copies of 2, provided t is sufficiently large.
In particular, our recursive construction allows us to effectively address
the two-table directed Oberwolfach problem. We show that OPβ(m1β,m2β) has
a solution for all 2β€m1ββ€m2β, with a definite exception of m1β=m2β=3
and a possible exception in the case that m1ββ{4,6}, m2β is even,
and m1β+m2ββ₯14. It has been shown previously that OPβ(m1β,m2β) has
a solution if m1β+m2β is odd, and that OPβ(m,m) has a solution if and
only if mξ =3.
In addition to solving many other cases of OPβ, we show that when 2β€m1β+β¦+mkββ€13, OPβ(m1β,β¦,mkβ) has a solution if and
only if (m1β,β¦,mkβ)ξ β{(4),(6),(3,3)} - Publication venue
- Schloss Dagstuhl - Leibniz-Zentrum fΓΌr Informatik GmbH, Dagstuhl Publishing
- Publication date
- 01/12/2018
- Field of study
- Publication venue
- 'Elsevier BV'
- Publication date
- Field of study
- Publication venue
- 'Elsevier BV'
- Publication date
- Field of study