## Abstract In 1960 Ore proved the following theorem: Let __G__ be a graph of order __n__. If __d__(__u__) + __d__(__v__)โฅ__n__ for every pair of nonadjacent vertices __u__ and __v__, then __G__ is hamiltonian. Since then for several other graph properties similar sufficient degree conditions have
Paths and cycles of hypergraphs
โ Scribed by Jianfang Wang; Tony T. Lee
- Publisher
- SP Science China Press
- Year
- 1999
- Tongue
- English
- Weight
- 638 KB
- Volume
- 42
- Category
- Article
- ISSN
- 1674-7283
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The square of a path (cycle) is the graph obtained by joining every pair of vertices of distance two in the path (cycle). Let \(G\) be a graph on \(n\) vertices with minimum degree \(\delta(G)\). Posa conjectured that if \(\delta(G) \geqslant \frac{2}{3} n\), then \(G\) contains the square of a hami
## Abstract Let __k__ be a positive integer, and __S__ a nonempty set of positive integers. Suppose that __G__ is a connected graph containing a path of length __k__, and that each path __P__ of length __k__ in __G__ is contained in some cycle __C__(__P__) of length s โ __S__. We prove that every p