Subpancyclicity of line graphs and degree sums along paths

Authors:
Liming Xiong;H. J. Broersma
Affiliations:
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China and Jiangxi Normal University, Nanchang 330027, PR China;Department of Computer Science, University of Durham DH1 3LE Durham, UK and Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, People's Republic of China
Venue:
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Year:
2006

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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 n=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.