We give counterexamples to two conjectures of Bill Jackson in Some remarks on arc-connectivity, vertex splitting, and orientation in graphs and digraphs (Journal of Graph Theory 12(3):429-436, 1988) concerning orientations of mixed graphs and splitting off in digraphs, and prove the first conjecture
A note on Hamiltonian split graphs
β Scribed by Rainer E Burkard; Peter L Hammer
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 230 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ β§ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ β __V__(__G__), then __G__ is hamiltonianβconnected. We generalize this result using set degrees.
Suppose G is a graph, F is a l-factor of G. G is called F-Hamiltonian, if there exists a Hamiltonian cycle containing F in G. In this paper, two necessary and sufficient conditions for a general graph and a bipartite graph being F-Hamiltonian are provided, respectively.