𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Locally Pancyclic Graphs

✍ 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.

✦ 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 ,


πŸ“œ SIMILAR VOLUMES


Pancyclic oriented graphs
✍ Zeng Min Song πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 324 KB

## Abstract Let __D__ be an oriented graph of order __n__ ≧ 9 and minimum degree __n__ βˆ’ 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__~^βˆ’^(__v__) ≧ __n__ βˆ’ 3.

Weakly pancyclic graphs
✍ Brandt, Stephan; Faudree, Ralph; Goddard, Wayne πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 517 KB

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

Weakly Pancyclic Graphs
✍ BΓ©la BollobΓ‘s; Andrew Thomason πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 145 KB

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 Γ‚4x+2 contains cycles of every length l, 3 l

Pancyclic subgraphs of random graphs
✍ Choongbum Lee; Wojciech Samotij πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 249 KB

## Abstract An __n__‐vertex graph is called pancyclic if it contains a cycle of length __t__ for all 3≀__t__≀__n__. In this article, we study pancyclicity of random graphs in the context of resilience, and prove that if __p__>__n__^βˆ’1/2^, then the random graph __G__(__n, p__) a.a.s. satisfies the f

Pancyclicity of connected circulant grap
✍ Bogdanowicz, Z. R. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 299 KB πŸ‘ 1 views

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

Locally semicomplete digraphs that are c
✍ Guo, Yubao; Volkmann, Lutz πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 923 KB

If A and Bare two subdigraphs of D, then we denote by &(A, 5) the distance between A and 5. Let D be a 2-connected locally semicomplete digraph on n 2 6 vertices. If S is a minimum separating set of D and d = min{do-s(N+(s) -S, N-(s) -S ) l s E S}, then rn = max(3, d + 2) I n/2 and D contains t w o