## Abstract Sufficient conditions on the degrees of a graph are given in order that its line graph have a hamiltonian cycle.
On hamiltonian line graphs
β Scribed by Lane Clark
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 191 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
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
It is shown that the existence of a Hamilton cycle in the line graph of a graph G can be ensured by imposing certain restrictions on certain induced subgraphs of G. Thereby a number of known results on hamiltonian line graphs are improved, including the earliest results in terms of vertex degrees. O
In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian
## Abstract In this paper, we show that if __G__ is a 3βedgeβconnected graph with $S \subseteq V(G)$ and $|S| \le 12$, then either __G__ has an Eulerian subgraph __H__ such that $S \subseteq V(H)$, or __G__ can be contracted to the Petersen graph in such a way that the preimage of each vertex of th