Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path
Liming Xiong, Hajo J. Broersma, Cornells Hoede · University of Twente Research Information · 2001
A graph is called {\\sl subpancyclic} if it contains a cycle of length $l$ for each $l$ between 3 and the circumference of a graph. We show that if $G$ is a connected graph on $n\\geq 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>\\frac{n+10}{2}$ for all four $u, v, x, y$ of a path $P=uvxy$ in $G, $ then its line graph is subpancyclic unless $G$ is isomorphic to an exceptional graph, and the result is best possible, even under the condition that $L(G)$ is hamiltonian.