On line graphs and the hamiltonian index
β Scribed by Ronald J. Gould
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 812 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
An extension of CI theorem of Chamhnd and Wall is obtained and, with it, a bound on the lamiltoniau index h(G) of a connected graph G (other than a path) is determined. As a tonsequence, it is
Fhown that if G is homogeneously traceable, then h(Gj ~2.
π SIMILAR VOLUMES
A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.
## Abstract Sufficient conditions on the degrees of a graph are given in order that its line graph have a hamiltonian cycle.
Using the contraction method, we find a best possible condition involving the minimum degree for a triangle-free graph to have a spanning eulerian subgraph.
It is shown that, if t is an integer !3 and not equal to 7 or 8, then there is a unique maximal graph having the path P t as a star complement for the eigenvalue Γ2: The maximal graph is the line graph of K m,m if t ΒΌ 2mΓ1, and of K m,m ΓΎ1 if t ΒΌ 2m. This result yields a characterization of L(G ) wh