A cycle C of a graph G is a D~-cycle if every component of G-V(C) has order less than 2. Using the notion of D~-cycles, a number of results are established concerning long cycles in graphs with prescribed toughness and minimum degree. Let G be a t-tough graph on n/> 3 vertices. If 6 > n/(t + 2) + 2-
Long cycles in subgraphs with prescribed minimum degree
β Scribed by L. Caccetta; K. Vijayan
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 621 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Caccetta,
L. and K. Vijayan, Long cycles in subgraphs with
π SIMILAR VOLUMES
## Abstract Our main result is the following theorem. Let __k__ββ₯β2 be an integer, __G__ be a graph of sufficiently large order __n__, and __Ξ΄__(__G__)ββ₯β__n__/__k__. Then: __G__ contains a cycle of length __t__ for every even integer __t__βββ[4, __Ξ΄__(__G__)β+β1]. If __G__ is nonbipartite then
## Abstract A graph __H__ is light in a given class of graphs if there is a constant __w__ such that every graph of the class which has a subgraph isomorphic to __H__ also has a subgraph isomorphic to __H__ whose sum of degrees in __G__ is β€β__w__. Let $\cal G$ be the class of simple planar graphs