Eigenvalues and edge-connectivity of regular graphs
✍ Scribed by Sebastian M. Cioabă
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 203 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In this article, we obtain a sufficient condition for the existence of regular factors in a regular graph in terms of its third largest eigenvalue. We also determine all values of __k__ such that every __r__‐regular graph with the third largest eigenvalue at most has a __k__‐factor.
Bill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is hamiltonian. It is shown in this paper that, under almost the same conditions as above, the graphs are edge-hamiltonian.
A cyclically m-edge-connected n-connected k-regular graph is called an (m.n.k) graph. It is proved that for any m > 0 and k 2 3, there is an (m, k, k) bipartite graph. A graph G is n-extendable if every matching of size n in G lies in a perfect matching of G. We prove the existence of a (k2-1, k + 1
Zhang, C.-Q. and Y.-J. Zhu, Long path connectivity of regular graphs, Discrete Mathematics 96 (1991) 151-160. Any pair of vertices in a 4-connected path or a path of length at least 3k-6. non-bipartite k-regular graph are joined bY a Hamilton \* This research was partially supported by AFOSR under g