Pairs of Heavy Subgraphs for Hamiltonicity of 2-Connected Graphs
✍ Scribed by Li, Binlong; Ryjáček, Zdeněk; Wang, Ying; Zhang, Shenggui
- Book ID
- 118197974
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2012
- Tongue
- English
- Weight
- 391 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0895-4801
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Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Zhu and Li showed that the upper bound 3k on n can be relaxed to q k if G is 3-connected and k 2 63. We improve both results by showing that G is hamiltonian if n 5 gk -7 and G does not belong to a res
## Abstract We characterize all pairs of connected graphs {__X__, __Y__} such that each 3‐connected {__X__, __Y__}‐free graph is pancyclic. In particular, we show that if each of the graphs in such a pair {__X__, __Y__} has at least four vertices, then one of them is the claw __K__~1,3~, while the