A Note on Asymmetric Hypergraphs

A k-graph G is asymmetric if there does not exist an automorphism on G other than the identity, and G is called minimal asymmetric if it is asymmetric but every non-trivial induced sub-hypergraph of G is non-asymmetric. Extending a result of Jiang and Nešetˇril (J Comb Theory Ser B 164: 105–118, 2024), we show that for every k ≥ 3, there exist infinitely many minimal asymmetric k-graphs which have maximum degree 2 and are linear. Further, we show that there are infinitely many 2-regular asymmetric k-graphs for k ≥ 3.