On Kotzig's conjecture for graphs with a regular path-connectedness
Anton Kotzig (see the book by J. A. Bondy and U. S. R. Murty (1976)) conjectured that there exists no graph with the property that every pair of vertices is connected by a unique path of length \(k\), \(k>2\). In this paper the authors prove the conjecture for \(k\geq 12\).
scientific article; zbMATH DE number 716474