## Abstract For a graph __G__, __p__(__G__) and __c__(__G__) denote the order of a longest path and a longest cycle of __G__, respectively. In this paper, we prove that if __G__ is a 3 βconnected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6
On longest cycles and strongly linking vertex sets
β Scribed by Bert Fassbender
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 245 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Let G be a simple non-hamiltonian graph, let C be a longest cycle in G, and let p be a positive integer. By considering a special form of connectivity, we obtain a sufficient condition on degrees for the nonexistence of ( p -1)-path-connected components in G -C.
π SIMILAR VOLUMES
Let G be an undirected connected graph with n nodes. A subset F of nodes of G is a feedback vertex set (fvs) if G -F is a forest and a subset J of nodes of G is a nonseparating independent set (nsis) if no two nodes of J are adjacent and G -J is connected. f(G), z ( G ) denote the cardinalities of a
## Abstract An inβtournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. Let __m__β=β4 or __m__β=β5 and let __D__ be a strongly connected inβtournament of order ${{n}}\geq {{2}}{{m}}-{{2}}$ such that each arc belongs to a directed path of order at