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On the Panconnectivity of Graphs with Large Degrees and Neighborhood Unions

โœ Scribed by B. Wei; Y. Zhu


Publisher
Springer Japan
Year
1998
Tongue
English
Weight
858 KB
Volume
14
Category
Article
ISSN
0911-0119

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๐Ÿ“œ SIMILAR VOLUMES


Long cycles in graphs with large degree
โœ Van den Heuvel, J. ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 801 KB

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.

Hamiltonian properties of graphs with la
โœ Douglas Bauer; Genghua Fan; Henk Jan Veldman ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 768 KB

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

Long dominating cycles and paths in grap
โœ H. J. Broersma; H. J. Veldman ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 413 KB ๐Ÿ‘ 1 views

## Abstract Let __G__ be a graph of order __n__ and define __NC(G)__ = min{|__N__(__u__) โˆช __N__(__v__)| |__uv__ โˆ‰ __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.

Neighborhood unions and the cycle cover
โœ Guantao Chen; Ronald J. Gould; Michael S. Jacobson; Richard H. Schelp ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 413 KB

## 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