Problems in graph theory: Graceful and sequential numberings of infinite graphs (Q1073813)

The author generalizes the concepts ''k-graceful'', ''graceful'' and ''k- sequential'' for countably infinite graphs \(G=(V,E)\) and proves some theorems. The most interesting theorem is the countably infinite version of the well-known Ringel-Kotzig conjecture for finite graphs, and it holds: All countably infinite trees are k-graceful for each \(k\geq 1\) (a 1-graceful graph is called graceful). He finishes his paper by giving six problems dealing with countably infinite graphs.