# An existence theorem on Hamiltonian $(g,f)$-factors in networks

Volume 11, Issue 1, pp 1--7 Publication Date: December 22, 2017       Article History
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### Authors

Sizhong Zhou - School of Science, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, P. R. China.

### Abstract

Let $a,b$, and $r$ be nonnegative integers with $\max\{3,r+1\}\leq a<b-r$, let $G$ be a graph of order $n$, and let $g$ and $f$ be two integer-valued functions defined on $V(G)$ with $\max\{3,r+1\}\leq a\leq g(x)<f(x)-r\leq b-r$ for any $x\in V(G)$. In this article, it is proved that if $n\geq\frac{(a+b-3)(a+b-5)+1}{a-1+r}$ and ${\rm bind}(G)\geq\frac{(a+b-3)(n-1)}{(a-1+r)n-(a+b-3)}$, then $G$ admits a Hamiltonian $(g,f)$-factor.

### Keywords

• Network
• graph
• binding number

•  05C70
•  05C45

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