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An s-Hamiltonian Line Graph Problem
Graphs and Combanatorics
  • Zhi-Hong Chen, Butler University
  • Wai-Chee Shiu
  • Deying Li
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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}.


“The final publication is available at Springer via”.

This is the pre-refereed version
Citation Information
An s-Hamiltonian Line Graph Problem, Graphs and Combinatorics 23, 241-248 (2007)