We present and prove several results concerning the length of longest cycles in 2connected or I-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings.
On the Panconnectivity of Graphs with Large Degrees and Neighborhood Unions
โ Scribed by B. Wei; Y. Zhu
- Publisher
- Springer Japan
- Year
- 1998
- Tongue
- English
- Weight
- 858 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Bauer, D., G. Fan and H.J. Veldman, Hamiltonian properties of graphs with large neighborhood unions, Discrete Mathematics 96 (1991) 33-49. Let G be a graph of order n, a k =min{~ki=ld(vi): {V 1 ..... Vn} is an independent set of vertices in G}, NC=min{IN(u) 13N(v)l:uv~E(G)} and NC2=min{IN(u) t3 wh
## Abstract Let __G__ be a graph of order __n__ and define __NC(G)__ = min{|__N__(__u__) โช __N__(__v__)| |__uv__ โ __E__(__G__)}. A cycle __C__ of __G__ is called a __dominating cycle__ or __D__โ__cycle__ if __V__(__G__) โ __V__(__C__) is an independent set. A __D__โ__path__ is defined analogously.
## Abstract For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a