## Abstract In this paper, __k__ + 1 real numbers __c__~1~, __c__~2~, β, __c__~__k__+1~ are found such that the following condition is sufficient for a __k__βconnected graph of order __n__ to be hamiltonian: for each independent vertex set of __k__ + 1 vertices in __G__. magnified image where S~i~
Degree with Neighborhood Conditions and Highly Hamiltonian Graphs
β Scribed by Zhao Kewen; Yue Lin; Ping Zhang
- Book ID
- 106334892
- Publisher
- Springer Netherlands
- Year
- 2008
- Tongue
- English
- Weight
- 247 KB
- Volume
- 109
- Category
- Article
- ISSN
- 0167-8019
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π SIMILAR VOLUMES
## Abstract For a positive integer __k__, a graph __G__ is __kβordered hamiltonian__ if for every ordered sequence of __k__ vertices there is a hamiltonian cycle that encounters the vertices of the sequence in the given order. It is shown that if __G__ is a graph of order __n__ with 3 β€ __k__ β€ __n
## Abstract Dirac proved that a graph __G__ is hamiltonian if the minimum degree $\delta(G) \geq n/2$, where __n__ is the order of __G__. Let __G__ be a graph and $A \subseteq V(G)$. The neighborhood of __A__ is $N(A)=\{ b: ab \in E(G)$ for some $a \in A\}$. For any positive integer __k__, we show
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