The infinite case of the edge-orbit conjecture (Q1122587)

\textit{L. Babai} [Discrete Math. 2, 295-307 (1972; Zbl 0238.05111); Lond. Math. Soc. Lect. Notes 52, 1-40 (1981; Zbl 0467.05031)] formulated the edge-orbit conjecture, which says: for any cardinal \(\kappa\), these exists a group G such that whenever \(G\cong Aut \Gamma\) for some graph \(\Gamma\), then Aut \(\Gamma\) has at least \(\kappa\) orbits on the edges of \(\Gamma\). The author proves this for a group G of uncountable regular cardinality \(\kappa\), leaving, according to Babai, the finite version open.