An existence theorem on Hamiltonian \((g,f)\)-factors in networks
Volume 11, Issue 1, pp 1--7
http://dx.doi.org/10.22436/jnsa.011.01.01
Publication Date: December 22, 2017
Submission Date: January 18, 2017
Revision Date: April 13, 2017
Accteptance Date: November 18, 2017
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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.
Share and Cite
ISRP Style
Sizhong Zhou, An existence theorem on Hamiltonian \((g,f)\)-factors in networks, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 1, 1--7
AMA Style
Zhou Sizhong, An existence theorem on Hamiltonian \((g,f)\)-factors in networks. J. Nonlinear Sci. Appl. (2018); 11(1):1--7
Chicago/Turabian Style
Zhou, Sizhong. "An existence theorem on Hamiltonian \((g,f)\)-factors in networks." Journal of Nonlinear Sciences and Applications, 11, no. 1 (2018): 1--7
Keywords
- Network
- graph
- binding number
MSC
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