On the spectrum of some cyclically and transitively oriented \( \mathcal{H} \)-designs
DOI:
https://doi.org/10.13069/jacodesmath.v13i2.392Keywords:
G-designs, H-designs, Uniform hypergraphsAbstract
This paper investigates oriented \( \mathcal{H} \)-designs on complete uniform hypergraphs of rank 3, focusing in particular on the spectrum of existence and on the construction of some cyclically and transitively oriented \( P^{(3)}(2,4) \)-designs and \( P^{(3)}(1,5) \)-designs, namely \( BCP^{(3)}(2,4) \)-designs and \( BCP^{(3)}(1,5) \)-designs for cyclically oriented ones, \( BTP^{(3)}(2,4) \)-designs and \( BTP^{(3)}(1,5) \)-designs for transitively oriented ones. In the appendix, we provide the python code to obtain the explicit realization of the \( BCP^{(3)}(2,4) \)-designs on \( v \) vertices. Moreover, the structure of this algorithm, with suitable modifications, can be generalized to the other three structures as well.
Accepted: 5 November 2025
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