## Abstract Let __D__ be an oriented graph of order __n__ β§ 9 and minimum degree __n__ β 2. This paper proves that __D__ is pancyclic if for any two vertices __u__ and __v__, either __uv__ β __A(D)__, or __d__~__D__~^+^(__u__) + __d__~__D__~^β^(__v__) β§ __n__ β 3.
Locally Pancyclic Graphs
β Scribed by Ladislav Stacho
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 215 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
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 ,
π SIMILAR VOLUMES
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
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 Γ4x+2 contains cycles of every length l, 3 l
## Abstract An __n__βvertex graph is called pancyclic if it contains a cycle of length __t__ for all 3β€__t__β€__n__. In this article, we study pancyclicity of random graphs in the context of resilience, and prove that if __p__>__n__^β1/2^, then the random graph __G__(__n, p__) a.a.s. satisfies the f
The circulant G,(al,. . . , ak), where 0 < al < ... < a k < ( n + 1 ) / 2 , is defined as the vertex-transitive graph that has vertices ifal,. . . ,if a k (mod n) adjacent to each vertex i. In this work we show that the connected circulants of degree at least three contain all even cycles. In additi
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