Subpancyclicity of line graphs and degree sums along paths

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Abstract

A graph is called subpancyclic if it contains a cycle of length for each between 3 and the circumference of the graph. We show that if G is a connected graph on n146 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.

MSC

05C45
05C35

Keywords

Degree sums
Line graph
Subpancyclicity
Pancyclic graph
Hamiltonian graph

Cited by (0)

This research has been supported by the Project for the Young Excellent Researchers of Beijing Institute of Technology and the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.