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On Traceable Line Graphs

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Abstract

Let G be a simple graph of order n and D 1(G) be the set of vertices of degree 1 in G. In this paper, we prove that if G − D 1(G) is 2-edge-connected and if for every edge \({xy \in E(G)}\) , max{d(x), d(y)} ≥ n/6−1, then for n large, L(G) is traceable with the exception of a class of well characterized graphs. A similar result in (Lai, Discrete Math 178:93–107, 1998) states that if we replace 6 by 5 in the above degree condition, then for n large, L(G) is Hamiltonian with the exception of a class of well characterized graphs.

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Authors and Affiliations

  1. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Zhaohong Niu & Liming Xiong

  2. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Zhaohong Niu

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  1. Zhaohong Niu
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  2. Liming Xiong
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Correspondence to Liming Xiong.

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Niu, Z., Xiong, L. On Traceable Line Graphs. Graphs and Combinatorics 31, 221–233 (2015). https://doi.org/10.1007/s00373-013-1371-3

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  • DOI: https://doi.org/10.1007/s00373-013-1371-3

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