Counting graph orientations with no directed triangles [article]

Pedro Araújo, Fábio Botler, Guilherme Oliveira Mota
2020 arXiv   pre-print
Alon and Yuster proved that the number of orientations of any n-vertex graph in which every K_3 is transitively oriented is at most 2^ n^2/4 for n ≥ 10^4 and conjectured that the precise lower bound on n should be n ≥ 8. We confirm their conjecture and, additionally, characterize the extremal families by showing that the balanced complete bipartite graph with n vertices is the only n-vertex graph for which there are exactly 2^ n^2/4 such orientations.
arXiv:2005.13091v1 fatcat:ljzwg2b27fb2hm25gzqpenk56m