Graphs where every maximal path is maximum
In 1974, C. Thomassen gave a characterization of all graphs in which each path is contained in a Hamiltonian path. Such graphs are of interest since they admit greedy algorithms for constructing Hamiltonian paths. For graphs without a Hamiltonian path, it is natural to ask whether each path is contained in a path of maximal length. In the present paper the author characterizes all connected graphs without a Hamiltonian path having this property.
scientific article; zbMATH DE number 934818