Document Type

Article

Publication Date

2007

Publication Title

Graphs and Combanatorics

First Page

241

Last Page

248

DOI

http://dx.doi.org/10.1007/s00373-007-0727-y

Abstract

For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In (J Graph Theory 11:399–407 (1987)), Broersma and Veldman proposed an open problem: for a given positive integer k, determine the value s for which the statement “Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected” is valid. Broersma and Veldman proved in 1987 that the statement above holds for 0 ≤ s ≤ k and asked, specifically, if the statement holds when s = 2k. In this paper, we prove that the statement above holds for 0 ≤ s ≤ max{2k, 6k − 16}.

Rights

“The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-007-0727-y”.

Notes

This is the pre-refereed version

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