×

zbMATH — the first resource for mathematics

Circuit double covers in special types of cubic graphs. (English) Zbl 1218.05129
Summary: Suppose that a 2-connected cubic graph \(G\) of order \(n\) has a circuit \(C\) of length at least \(n - 4\) such that \(G - V(C)\) is connected. We show that \(G\) has a circuit double cover containing a prescribed set of circuits which satisfy certain conditions. It follows that hypohamiltonian cubic graphs (i.e., non-hamiltonian cubic graphs \(G\) such that \(G - v\) is hamiltonian for every \(v\in V(G))\) have strong circuit double covers.

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C40 Connectivity
05C38 Paths and cycles
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fleischner, H., Eulersche linien und kreisüberdeckungen, die vorgegebene durchgänge in den kanten vermeiden, Jct b, 29, 2, 145-167, (1980) · Zbl 0438.05041
[2] Fleischner, H., Cycle decompositions, 2-coverings, removable cycles, and the four-color-disease, (), 233-246
[3] Fleischner, H., Proof of the strong 2-cover conjecture for planar graphs, Jct b, 40, 2, 229-230, (1986) · Zbl 0587.05041
[4] H. Fleischner, Eulerian Graphs and Related Topics, Part 1, Vol. 1, Annals of Discrete Mathematics, vol. 45, Amsterdam, 1990 · Zbl 0792.05091
[5] Fleischner, H., Uniqueness of maximal dominating cycles in 3-regular graphs and of Hamiltonian cycles in 4-regular graphs, J. graph theory, 18, 5, 449-459, (1994) · Zbl 0807.05050
[6] H. Fleischner, Uniquely Hamiltonian graphs of minimum degree four (submitted for publication) · Zbl 1280.05074
[7] R.L. Graham, M. Grötschel, L. Lovász (Eds.), Handbook of Combinatorics, vol. 1, Amsterdam, 1995
[8] Tutte, W.T., On Hamiltonian circuits, J. London math. soc., 21, 98-101, (1946) · Zbl 0061.41306
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.