Dirac proved that if each vertex of a graph G of order n 23 has degree at least n/2, then the graph is Hamiltonian. This result will be generalized by showing that if the union of the neighborhoods of each pair of vertices of a 2connected graph G of sufficiently large order n has at least n/2 vertic
A generalization of dirac’s theorem
✍ Scribed by Stephen C. Locke
- Book ID
- 110564422
- Publisher
- Springer-Verlag
- Year
- 1985
- Tongue
- English
- Weight
- 520 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0209-9683
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📜 SIMILAR VOLUMES
In this paper, we give a generalization of a well-known result of Dirac that given any k vertices in a k-connected graph where k 2, there is a circuit containing all of them. We also generalize a result of Ha ggkvist and Thomassen. Our main result partially answers an open matroid question of Oxley.
In our study of the extremities of a graph, we define a moplex as a maximal clique module the neighborhood of which is a minimal separator of the graph. This notion enables us to strengthen Dirac's theorem : "Every non-clique triangulated graph has at least two non-adjacent simplicial vertices", res