Odd Cycle Transversals and Independent Sets in Fullerene Graphs
✍ Scribed by Faria, Luerbio; Klein, Sulamita; Stehlík, Matěj
- Book ID
- 118197186
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2012
- Tongue
- English
- Weight
- 298 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0895-4801
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📜 SIMILAR VOLUMES
In 1975, John Sheehan conjectured that every Hamiltonian 4-regular graph has a second Hamiltonian cycle. Combined with earlier results this would imply that every Hamiltonian r-regular graph (r 3) has a second Hamiltonian cycle. We shall verify this for r 300.
In this paper, we determine the largest number of maximal independent sets among all connected graphs of order n, which contain at most one cycle. We also characterize those extremal graphs achieving this maximum value. As a consequence, the corresponding results for graphs with at most one cycle bu
## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G.__ In this paper, we determine the maximum number of maximal independent sets among all bipartite graphs of order __n__ and the extremal graphs as well as