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Zbl 0651.05049
Veldman, H.J.
A result on Hamiltonian line graphs involving restrictions on induced subgraphs.
(English)
[J] J. Graph Theory 12, No.3, 413-420 (1988). ISSN 0364-9024; ISSN 1097-0118/e

Author's abstract: It is shown that the existence of a Hamilton cycle in the line graph of a graph G can be ensured by imposing certain restrictions on certain induced subgraphs of G. Thereby a number of known results on Hamiltonian line graphs are improved, including the earliest results in terms of vertex degrees. One particular consequence is that every graph of diameter 2 and order at least 4 has a Hamiltonian line graph.'' \par As a consequence of the main result in this paper it is deduced that L(G) is Hamiltonian for every graph G of order $n\ge 4$ such that $d(u)+d(v)\ge n-1$ holds either for every pair u, v of nonadjacent vertices, either for every edge uv$\in E(G)\ne \emptyset$ whenever $G\not\cong P\sb 4$.
[I.Tomescu]
MSC 2000:
*05C45 Eulerian and Hamiltonian graphs
05C99 Graph theory

Keywords: induced subgraphs; Hamiltonian line graphs

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