Let f (n) be the minimum number of cycles present in a 3-connected cubic graph on n vertices. In 1986, C. A. Barefoot, L. Clark, and R. Entringer (Congr. Numer. 53, 1986) showed that f (n) is subexponential and conjectured that f (n) is superpolynomial. We verify this by showing that, for n sufficie
The number of cycles in 2-factors of cubic graphs
β Scribed by Moshe Rosenfeld
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 758 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
We describe a general sufficient condition for a Hamiltonian graph to contain another Hamiltonian cycle. We apply it to prove that every longest cycle in a 3-connected cubic graph has a chord. We also verify special cases of an old conjecture of Sheehan on Hamiltonian cycles in 4-regular graphs and
## Abstract Let __G__ be a simple graph with order __n__ and minimum degree at least two. In this paper, we prove that if every odd branchβbond in __G__ has an edgeβbranch, then its line graph has a 2βfactor with at most ${{3n - 2}\over {8}}$ components. For a simple graph with minimum degree at le
Let G(V , E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I 1 ΓI 2 Γβ’ β’ β’ΓI b , where each I i is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G), is the minimum positive in