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

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.


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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


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