Subpancyclicity of line graphs and degree sums along paths


Xiong, L. and Broersma, H.J. (2006) Subpancyclicity of line graphs and degree sums along paths. Discrete Applied Mathematics, 154 (9). pp. 1453-1463. ISSN 0166-218X

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Abstract:A graph is called subpancyclic if it contains a cycle of length $\ell$ for each $\ell$ between 3 and the circumference of the graph. We show that if $G$ is a connected graph on $n\ge 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>(n+10/2)$ for all four vertices $u,v,x,y$ of any path $P=uvxy$ in $G$, then the line graph $L(G)$ is subpancyclic, unless $G$ is isomorphic to an exceptional graph. Moreover, we show that this result is best possible, even under the assumption that $L(G)$ is hamiltonian. This improves earlier sufficient conditions by a multiplicative factor rather than an additive constant.

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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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