# zbMATH — the first resource for mathematics

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

##### MSC:
 05C45 Eulerian and Hamiltonian graphs
##### Keywords:
Hamiltonian cycle
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.