3‐Connected line graphs of triangular graphs are panconnected and 1‐hamiltonian
Hajo J. Broersma, H.J. Veldman · Journal of Graph Theory · 1987
Abstract A graph is k‐triangular if each edge is in at least k triangles. Triangular is a synonym for 1‐triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3‐connected. Furthermore, the line graph of a k‐triangular graph is k‐hamiltonian if and only if it is (k + 2)‐connected (k ⩾ 1). These results generalize work of Clark and Wormald and of Lesniak‐Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.