Towards Nash‐Williams orientation conjecture for infinite graphs
Amena Assem · Journal of Graph Theory · 2024
Abstract In 1960 Nash‐Williams proved that an edge‐connectivity of is sufficient for a finite graph to have a ‐arc‐connected orientation. He then conjectured that the same is true for infinite graphs. In 2016, Thomassen, using his own results on the auxiliary lifting graph, proved that ‐edge‐connected infinite graphs admit a ‐arc‐connected orientation. Here we improve this result for the class of one‐ended locally finite graphs and show that an edge‐connectivity of is enough in that case. Crucial to this improvement are results presented in a separate paper, by the same author of this paper, on the key concept of the lifting graph, extending results by Ok, Richter, and Thomassen.