The most general structure of graphs with hamiltonian or hamiltonian connected square

J. Ekstein; H. Fleischner

doi:10.1016/j.disc.2023.113702

paper

The most general structure of graphs with hamiltonian or hamiltonian connected square

arXiv:2203.12665 · doi:10.1016/j.disc.2023.113702

Abstract

On the basis of recent results on hamiltonicity and hamiltonian connectedness in the square of a 2-block, we determine the most general block-cutvertex structure a graph $G$ may have in order to guarantee that $G^{2}$ is hamiltonian, hamiltonian connected, respectively. Such an approach was already developed for hamiltonian total graphs.

18 pages