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


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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