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.
Original language | English |
---|---|
Pages (from-to) | 399-407 |
Journal | Journal of graph theory |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1987 |