@article {IOPORT.00734473, author = {Lai, Hong-Jian and Zhang, Cun-Quan}, title = {Hamiltonian connected line graphs.}, year = {1994}, journal = {Ars Combinatoria}, volume = {38}, issn = {0381-7032}, pages = {193-202}, publisher = {Charles Babbage Research Centre, Winnipeg, MB}, abstract = {A trail $T$ in $G$ whose first edge is $e$ and whose last edge is $e'$ and for which $V(T)= V(G)$ is called a spanning $(e, e')$-trail. Authors have proven for graphs with edge connectivity $\kappa'(G)\ge 2$ that if for every pair of nonadjacent vertices $u, v\in G$, $d(u)+ d(v)> \textstyle{{2n\over 3}}- 2,$ then for every pair of edges $e, e'\in E(G)$, exactly one of the following holds: (i) $G$ has spanning $(e,e')$- trail. (ii) $\{e, e'\}$ is an essential edge-cut of $G$. They have also established that the problem to determine if $G$ has a spanning $(e, e')$-trail is NP-complete.}, reviewer = {P.Sekanina (Fairbanks)}, identifier = {00734473}, }