Hamiltonian pancyclic graphs
✍ Scribed by Denise Amar; Evelyne Flandrin; Irène Fournier; Anne Germa
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 79 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In answer to a question of Erdős, we show that a Hamiltonian weakly-pancyclic graph of order n can have girth as large as about 2 n/ log n. In contrast to this, we show that the existence of
## Abstract Let __D__ be an oriented graph of order __n__ ≧ 9 and minimum degree __n__ − 2. This paper proves that __D__ is pancyclic if for any two vertices __u__ and __v__, either __uv__ ≅ __A(D)__, or __d__~__D__~^+^(__u__) + __d__~__D__~^−^(__v__) ≧ __n__ − 3.
In generalizing the concept of a pancyclic graph, we say that a graph is ''weakly pancyclic'' if it contains cycles of every length between the length of a shortest and a longest cycle. In this paper it is shown that in many cases the requirements on a graph which ensure that it is weakly pancyclic
We prove the following theorem. Let G be a graph of order n and let W V(G). If |W | 3 and d G (x)+d G ( y) n for every pair of non-adjacent vertices x, y # W, then either G contains cycles C 3 ,
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. A substantial result of Ha ggkvist, Faudree, and Schelp (1981) states that a Hamiltonian non-bipartite graph of order n and size at least w(n&1) 2 Â4x+2 contains cycles of every length l, 3 l