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On the Hamiltonian index. (English) Zbl 0638.05034
The author defines h(G) as the smallest number m such that the m times iterated line graph has a Hamiltonian cycle and \(\ell (G)\) as the largest number k such that G has a path of length k which is not part of a \(K_ 3\) and whose internal vertices all have degree 2 in G. Theorem: h(G)\(\leq \ell (G)+1\) for every connected graph G which is not a path.
Reviewer: C.Thomassen

05C45 Eulerian and Hamiltonian graphs
Full Text: DOI
[1] Bondy, A.; Murty, U.S.R., Graph theory with applications, (1976), Elsevier New York · Zbl 1226.05083
[2] P.A. Catlin, Removing forests to find spanning Eulerian subgraphs, preprint. · Zbl 0659.05073
[3] Chartrand, G., On Hamiltonian line graphs, Trans. amer. math. soc., 134, 3, 559-566, (1968) · Zbl 0169.55405
[4] Chartrand, G.; Wall, C.E., On the Hamiltonian index of a graph, Studia. sci. math. hung., 8, 43-48, (1973) · Zbl 0279.05121
[5] Gould, R.J., On line graphs and the Hamiltonian index, Discrete math., 34, 111-117, (1981) · Zbl 0451.05031
[6] Harary, F.; Nash-Williams, C.St.J.A., On eulerian and Hamiltonian graphs and line graphs, Canad. math. bull., 9, 701-710, (1965) · Zbl 0136.44704
[7] Lesniak-Foster, L.; Williamson, J.E., On spanning and dominating circuits in graphs, Canad. math. bull., 20, 215-220, (1977) · Zbl 0357.05060
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