@book{a143b1a9c71a44dc959cdbdde4efbf9d,

title = "Subpancyclicity in the line graph of a graph with large degree sums of vertices along a path",

abstract = "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.",

keywords = "MSC-05C45, MSC-05C35",

author = "L. Xiong and H.J. Broersma and C. Hoede",

year = "2001",

language = "English",

series = "Memorandum",

publisher = "University of Twente",

number = "1606",

address = "Netherlands",

}